WildeThing

I agree with Old Bill, under the assumption that you are hoping to use the thesis for your WS. The WS is one of your key documents so if you don't have a paper you can use, a thesis would be a good way to accomplish that (assuming you'd have it finalized and feedback-ed by the application deadline). However, if you're taking grad classes, you might already have a WS you can use (and seminar papers fit the length better, so it will be easier to cut them down and polish them). If you do have a strong seminar paper I would actually recommend doing comps.
Comps were both the hardest and most rewarding experience for me in the PhD. They're a great opportunity to read the things you've been meaning to read, think you have to read, or should read for breadth/specialization. My dissertation idea came from this process and has nothing to do with the things I applied to do. By its very nature, if you read across your field (and adjacent fields) you will discover a lot of interesting things and you will be better versed to make research claims about it. While I was successful on the grad application trail, I think that had I had this type of experience and knowledge when I applied I would have been even more successful.
Note that this will depend on what the structure of comps are. Are you forced to pick from an assigned list? Do you have freedom to choose what you want? In my case, I had a lot of freedom to pick what I wanted to read, but people who did lists in other fields faced some limitations. This is especially a good opportunity to read some theory and new scholarship in your field, if the structure allows for it.
Again, this would be most useful if you can do the comps before you apply so you can use this knowledge. So, ultimately, I would think about whether you feel comfortable with your WS and how dates work out, and then think about how either route would help you compose your other documents (breadth could help with your SoP, but a thesis could also help (and a thesis MIGHT get you a stronger letter of recommendation, depending on your advisor experience)), and finally you could think about what you think would help you most as a PhD student.
All of this is based on the assumption that you are applying to PhDs. If you might be leaving academia with the MA, the considerations will be different (not sure if this would even matter).

I agree with Old Bill, under the assumption that you are hoping to use the thesis for your WS. The WS is one of your key documents so if you don't have a paper you can use, a thesis would be a good way to accomplish that (assuming you'd have it finalized and feedback-ed by the application deadline). However, if you're taking grad classes, you might already have a WS you can use (and seminar papers fit the length better, so it will be easier to cut them down and polish them). If you do have a strong seminar paper I would actually recommend doing comps.
Comps were both the hardest and most rewarding experience for me in the PhD. They're a great opportunity to read the things you've been meaning to read, think you have to read, or should read for breadth/specialization. My dissertation idea came from this process and has nothing to do with the things I applied to do. By its very nature, if you read across your field (and adjacent fields) you will discover a lot of interesting things and you will be better versed to make research claims about it. While I was successful on the grad application trail, I think that had I had this type of experience and knowledge when I applied I would have been even more successful.
Note that this will depend on what the structure of comps are. Are you forced to pick from an assigned list? Do you have freedom to choose what you want? In my case, I had a lot of freedom to pick what I wanted to read, but people who did lists in other fields faced some limitations. This is especially a good opportunity to read some theory and new scholarship in your field, if the structure allows for it.
Again, this would be most useful if you can do the comps before you apply so you can use this knowledge. So, ultimately, I would think about whether you feel comfortable with your WS and how dates work out, and then think about how either route would help you compose your other documents (breadth could help with your SoP, but a thesis could also help (and a thesis MIGHT get you a stronger letter of recommendation, depending on your advisor experience)), and finally you could think about what you think would help you most as a PhD student.
All of this is based on the assumption that you are applying to PhDs. If you might be leaving academia with the MA, the considerations will be different (not sure if this would even matter).

I would not listen to this advice. Once you’re in there is no difference between being a direct admit or an off-the-waitlist person. There’s a lot of reasons why you might be waitlisted one place and accepted another and it’s not necessarily a matter of fit. Do not take yourself off a waitlist unless you are sure you would not take their offer anyway. 
To the original question, you can and should email them to say that you are still interested but that you have another offer and ask if they can give you any more information (e.g. is the waitlist ranked or by area? where do you stand on it? are they waiting on many responses or have most people accepted already? do they expect to hear back or respond to you by a certain date (e.g. after visit days), etc.). None of these answers will actually help you get in (nor will having another offer) but at least you’ll have some info.
If you have a strong sense that you might take the waitlist offer if it is made, I would just hold on until the deadline (and follow up with the waitlist). The other school knows this is a thing and will respect it. There is still more than a month to go and often waitlist movement happens at the very end.

I'm really sorry about your rejections, being shut out is really rough. I would strongly advise against going into debt for any graduate program, especially when it's not a prerequisite for entry for your next stage. While many PhD admits have MAs, there are also many that don't (not sure what the actual breakdown is). Having an MA would not necessarily make you more competitive, but it does put a burden on you to make a decent living once you're hopefully out of the PhD and while the market might change dramatically by then, right now that is not a guarantee, as many of the jobs currently offered (which do not cover the labor pool) are equivalent to graduate stipends, which are generally around minimum wage.
Your best bet is to take a beat to reassess and try to think what, out of the things you have control over, might have hindered your chances and then attempt to address that in the next round (and you might want to look into things like the Institute for the Recruitment of Teachers for support in the next cycle). What MAs are good for, assuming you make good use of them, is a. demonstrating an ability to do graduate-level work, b. developing a more sophisticated understanding of the field, c. giving you opportunities to develop and execute on ideas, and d. offer you an extended pool of faculty and colleagues who can support you (I'm sure there are other things, but I think these are the main ones). None of these things are necessary, and some of them are things you can do on your own. While having a wider network of support is hard to replicate outside of an institution, if you're able to, you can spend this time reading and developing your ideas, and the WS you submit would override any graduate experience anyway. The best thing you can do is polish your SoP and WS over the coming year.
If you were considering funded MAs my answer would be different, but given the prerequisites for grad admissions and the realities of job market on the other side, we are currently debating whether graduate programs themselves are worth it, so unfunded ones are definitely not.

I'm really sorry about your rejections, being shut out is really rough. I would strongly advise against going into debt for any graduate program, especially when it's not a prerequisite for entry for your next stage. While many PhD admits have MAs, there are also many that don't (not sure what the actual breakdown is). Having an MA would not necessarily make you more competitive, but it does put a burden on you to make a decent living once you're hopefully out of the PhD and while the market might change dramatically by then, right now that is not a guarantee, as many of the jobs currently offered (which do not cover the labor pool) are equivalent to graduate stipends, which are generally around minimum wage.
Your best bet is to take a beat to reassess and try to think what, out of the things you have control over, might have hindered your chances and then attempt to address that in the next round (and you might want to look into things like the Institute for the Recruitment of Teachers for support in the next cycle). What MAs are good for, assuming you make good use of them, is a. demonstrating an ability to do graduate-level work, b. developing a more sophisticated understanding of the field, c. giving you opportunities to develop and execute on ideas, and d. offer you an extended pool of faculty and colleagues who can support you (I'm sure there are other things, but I think these are the main ones). None of these things are necessary, and some of them are things you can do on your own. While having a wider network of support is hard to replicate outside of an institution, if you're able to, you can spend this time reading and developing your ideas, and the WS you submit would override any graduate experience anyway. The best thing you can do is polish your SoP and WS over the coming year.
If you were considering funded MAs my answer would be different, but given the prerequisites for grad admissions and the realities of job market on the other side, we are currently debating whether graduate programs themselves are worth it, so unfunded ones are definitely not.

I'm really sorry about your rejections, being shut out is really rough. I would strongly advise against going into debt for any graduate program, especially when it's not a prerequisite for entry for your next stage. While many PhD admits have MAs, there are also many that don't (not sure what the actual breakdown is). Having an MA would not necessarily make you more competitive, but it does put a burden on you to make a decent living once you're hopefully out of the PhD and while the market might change dramatically by then, right now that is not a guarantee, as many of the jobs currently offered (which do not cover the labor pool) are equivalent to graduate stipends, which are generally around minimum wage.
Your best bet is to take a beat to reassess and try to think what, out of the things you have control over, might have hindered your chances and then attempt to address that in the next round (and you might want to look into things like the Institute for the Recruitment of Teachers for support in the next cycle). What MAs are good for, assuming you make good use of them, is a. demonstrating an ability to do graduate-level work, b. developing a more sophisticated understanding of the field, c. giving you opportunities to develop and execute on ideas, and d. offer you an extended pool of faculty and colleagues who can support you (I'm sure there are other things, but I think these are the main ones). None of these things are necessary, and some of them are things you can do on your own. While having a wider network of support is hard to replicate outside of an institution, if you're able to, you can spend this time reading and developing your ideas, and the WS you submit would override any graduate experience anyway. The best thing you can do is polish your SoP and WS over the coming year.
If you were considering funded MAs my answer would be different, but given the prerequisites for grad admissions and the realities of job market on the other side, we are currently debating whether graduate programs themselves are worth it, so unfunded ones are definitely not.

I'm really sorry about your rejections, being shut out is really rough. I would strongly advise against going into debt for any graduate program, especially when it's not a prerequisite for entry for your next stage. While many PhD admits have MAs, there are also many that don't (not sure what the actual breakdown is). Having an MA would not necessarily make you more competitive, but it does put a burden on you to make a decent living once you're hopefully out of the PhD and while the market might change dramatically by then, right now that is not a guarantee, as many of the jobs currently offered (which do not cover the labor pool) are equivalent to graduate stipends, which are generally around minimum wage.
Your best bet is to take a beat to reassess and try to think what, out of the things you have control over, might have hindered your chances and then attempt to address that in the next round (and you might want to look into things like the Institute for the Recruitment of Teachers for support in the next cycle). What MAs are good for, assuming you make good use of them, is a. demonstrating an ability to do graduate-level work, b. developing a more sophisticated understanding of the field, c. giving you opportunities to develop and execute on ideas, and d. offer you an extended pool of faculty and colleagues who can support you (I'm sure there are other things, but I think these are the main ones). None of these things are necessary, and some of them are things you can do on your own. While having a wider network of support is hard to replicate outside of an institution, if you're able to, you can spend this time reading and developing your ideas, and the WS you submit would override any graduate experience anyway. The best thing you can do is polish your SoP and WS over the coming year.
If you were considering funded MAs my answer would be different, but given the prerequisites for grad admissions and the realities of job market on the other side, we are currently debating whether graduate programs themselves are worth it, so unfunded ones are definitely not.

I'm really sorry about your rejections, being shut out is really rough. I would strongly advise against going into debt for any graduate program, especially when it's not a prerequisite for entry for your next stage. While many PhD admits have MAs, there are also many that don't (not sure what the actual breakdown is). Having an MA would not necessarily make you more competitive, but it does put a burden on you to make a decent living once you're hopefully out of the PhD and while the market might change dramatically by then, right now that is not a guarantee, as many of the jobs currently offered (which do not cover the labor pool) are equivalent to graduate stipends, which are generally around minimum wage.
Your best bet is to take a beat to reassess and try to think what, out of the things you have control over, might have hindered your chances and then attempt to address that in the next round (and you might want to look into things like the Institute for the Recruitment of Teachers for support in the next cycle). What MAs are good for, assuming you make good use of them, is a. demonstrating an ability to do graduate-level work, b. developing a more sophisticated understanding of the field, c. giving you opportunities to develop and execute on ideas, and d. offer you an extended pool of faculty and colleagues who can support you (I'm sure there are other things, but I think these are the main ones). None of these things are necessary, and some of them are things you can do on your own. While having a wider network of support is hard to replicate outside of an institution, if you're able to, you can spend this time reading and developing your ideas, and the WS you submit would override any graduate experience anyway. The best thing you can do is polish your SoP and WS over the coming year.
If you were considering funded MAs my answer would be different, but given the prerequisites for grad admissions and the realities of job market on the other side, we are currently debating whether graduate programs themselves are worth it, so unfunded ones are definitely not.

I would not listen to this advice. Once you’re in there is no difference between being a direct admit or an off-the-waitlist person. There’s a lot of reasons why you might be waitlisted one place and accepted another and it’s not necessarily a matter of fit. Do not take yourself off a waitlist unless you are sure you would not take their offer anyway. 
To the original question, you can and should email them to say that you are still interested but that you have another offer and ask if they can give you any more information (e.g. is the waitlist ranked or by area? where do you stand on it? are they waiting on many responses or have most people accepted already? do they expect to hear back or respond to you by a certain date (e.g. after visit days), etc.). None of these answers will actually help you get in (nor will having another offer) but at least you’ll have some info.
If you have a strong sense that you might take the waitlist offer if it is made, I would just hold on until the deadline (and follow up with the waitlist). The other school knows this is a thing and will respect it. There is still more than a month to go and often waitlist movement happens at the very end.

I think maybe you should consider your own advice (and also read the OP's post). They asked about studying at two different universities, not a dual degree. While this is technically possible, as an international student there are many loopholes one would have to jump through (here's just an example from one institution), which can make this practically unfeasible (if it is actually feasible, UMich for instance, would require part-time enrollment in both programs, which can be a tremendous roadblock for many administrative reasons). I feel like sometimes domestic students aren't fully aware of the limitations of being an international student; contrary to what another poster has said, visa status IS the foremost concern for an international student, and dismissing these concerns for incoming students can produce a lot of headaches later on (I cannot begin to describe how much bullshit you can go through as an international student doing basic things like just receiving your stipend, accepting your offer-letter employment, etc.). Of course, if you can get into a dual program then most of the concerns go out of the window because the structure is in place; but, again, this is not what OP, who was already in a PhD program, was discussing and thus is not relevant (for them, but certainly helpful for future readers).

As of 12/23:

Applications out: MIT EECS, Stanford BMI, UCSF BMI, Penn GCB, Harvard SSQB, Tri-I CBM, UCLA Genetics and Genomics Track, MSSM Biomed Sci, and Emory PBEE
Interview Invites Received: UCLA (12/9), UCSF (12/12), Stanford (12/16), Penn (12/21), and Emory (12/22)
From what I've gathered, it seems like I'm probably out on Harvard, but I'm not sure w/r/t Tri-I, MSSM (invites probably come out January), and MIT (app deadline was 12/15 and it's a huge program. EECS dept calendar has "Grad Admissions Round Up" scheduled for 1/18-1/24).
 

I would not listen to this advice. Once you’re in there is no difference between being a direct admit or an off-the-waitlist person. There’s a lot of reasons why you might be waitlisted one place and accepted another and it’s not necessarily a matter of fit. Do not take yourself off a waitlist unless you are sure you would not take their offer anyway. 
To the original question, you can and should email them to say that you are still interested but that you have another offer and ask if they can give you any more information (e.g. is the waitlist ranked or by area? where do you stand on it? are they waiting on many responses or have most people accepted already? do they expect to hear back or respond to you by a certain date (e.g. after visit days), etc.). None of these answers will actually help you get in (nor will having another offer) but at least you’ll have some info.
If you have a strong sense that you might take the waitlist offer if it is made, I would just hold on until the deadline (and follow up with the waitlist). The other school knows this is a thing and will respect it. There is still more than a month to go and often waitlist movement happens at the very end.

I would not listen to this advice. Once you’re in there is no difference between being a direct admit or an off-the-waitlist person. There’s a lot of reasons why you might be waitlisted one place and accepted another and it’s not necessarily a matter of fit. Do not take yourself off a waitlist unless you are sure you would not take their offer anyway. 
To the original question, you can and should email them to say that you are still interested but that you have another offer and ask if they can give you any more information (e.g. is the waitlist ranked or by area? where do you stand on it? are they waiting on many responses or have most people accepted already? do they expect to hear back or respond to you by a certain date (e.g. after visit days), etc.). None of these answers will actually help you get in (nor will having another offer) but at least you’ll have some info.
If you have a strong sense that you might take the waitlist offer if it is made, I would just hold on until the deadline (and follow up with the waitlist). The other school knows this is a thing and will respect it. There is still more than a month to go and often waitlist movement happens at the very end.

I would not listen to this advice. Once you’re in there is no difference between being a direct admit or an off-the-waitlist person. There’s a lot of reasons why you might be waitlisted one place and accepted another and it’s not necessarily a matter of fit. Do not take yourself off a waitlist unless you are sure you would not take their offer anyway. 
To the original question, you can and should email them to say that you are still interested but that you have another offer and ask if they can give you any more information (e.g. is the waitlist ranked or by area? where do you stand on it? are they waiting on many responses or have most people accepted already? do they expect to hear back or respond to you by a certain date (e.g. after visit days), etc.). None of these answers will actually help you get in (nor will having another offer) but at least you’ll have some info.
If you have a strong sense that you might take the waitlist offer if it is made, I would just hold on until the deadline (and follow up with the waitlist). The other school knows this is a thing and will respect it. There is still more than a month to go and often waitlist movement happens at the very end.

I would not listen to this advice. Once you’re in there is no difference between being a direct admit or an off-the-waitlist person. There’s a lot of reasons why you might be waitlisted one place and accepted another and it’s not necessarily a matter of fit. Do not take yourself off a waitlist unless you are sure you would not take their offer anyway. 
To the original question, you can and should email them to say that you are still interested but that you have another offer and ask if they can give you any more information (e.g. is the waitlist ranked or by area? where do you stand on it? are they waiting on many responses or have most people accepted already? do they expect to hear back or respond to you by a certain date (e.g. after visit days), etc.). None of these answers will actually help you get in (nor will having another offer) but at least you’ll have some info.
If you have a strong sense that you might take the waitlist offer if it is made, I would just hold on until the deadline (and follow up with the waitlist). The other school knows this is a thing and will respect it. There is still more than a month to go and often waitlist movement happens at the very end.

I would not listen to this advice. Once you’re in there is no difference between being a direct admit or an off-the-waitlist person. There’s a lot of reasons why you might be waitlisted one place and accepted another and it’s not necessarily a matter of fit. Do not take yourself off a waitlist unless you are sure you would not take their offer anyway. 
To the original question, you can and should email them to say that you are still interested but that you have another offer and ask if they can give you any more information (e.g. is the waitlist ranked or by area? where do you stand on it? are they waiting on many responses or have most people accepted already? do they expect to hear back or respond to you by a certain date (e.g. after visit days), etc.). None of these answers will actually help you get in (nor will having another offer) but at least you’ll have some info.
If you have a strong sense that you might take the waitlist offer if it is made, I would just hold on until the deadline (and follow up with the waitlist). The other school knows this is a thing and will respect it. There is still more than a month to go and often waitlist movement happens at the very end.

I would not listen to this advice. Once you’re in there is no difference between being a direct admit or an off-the-waitlist person. There’s a lot of reasons why you might be waitlisted one place and accepted another and it’s not necessarily a matter of fit. Do not take yourself off a waitlist unless you are sure you would not take their offer anyway. 
To the original question, you can and should email them to say that you are still interested but that you have another offer and ask if they can give you any more information (e.g. is the waitlist ranked or by area? where do you stand on it? are they waiting on many responses or have most people accepted already? do they expect to hear back or respond to you by a certain date (e.g. after visit days), etc.). None of these answers will actually help you get in (nor will having another offer) but at least you’ll have some info.
If you have a strong sense that you might take the waitlist offer if it is made, I would just hold on until the deadline (and follow up with the waitlist). The other school knows this is a thing and will respect it. There is still more than a month to go and often waitlist movement happens at the very end.

I would not listen to this advice. Once you’re in there is no difference between being a direct admit or an off-the-waitlist person. There’s a lot of reasons why you might be waitlisted one place and accepted another and it’s not necessarily a matter of fit. Do not take yourself off a waitlist unless you are sure you would not take their offer anyway. 
To the original question, you can and should email them to say that you are still interested but that you have another offer and ask if they can give you any more information (e.g. is the waitlist ranked or by area? where do you stand on it? are they waiting on many responses or have most people accepted already? do they expect to hear back or respond to you by a certain date (e.g. after visit days), etc.). None of these answers will actually help you get in (nor will having another offer) but at least you’ll have some info.
If you have a strong sense that you might take the waitlist offer if it is made, I would just hold on until the deadline (and follow up with the waitlist). The other school knows this is a thing and will respect it. There is still more than a month to go and often waitlist movement happens at the very end.

I would not listen to this advice. Once you’re in there is no difference between being a direct admit or an off-the-waitlist person. There’s a lot of reasons why you might be waitlisted one place and accepted another and it’s not necessarily a matter of fit. Do not take yourself off a waitlist unless you are sure you would not take their offer anyway. 
To the original question, you can and should email them to say that you are still interested but that you have another offer and ask if they can give you any more information (e.g. is the waitlist ranked or by area? where do you stand on it? are they waiting on many responses or have most people accepted already? do they expect to hear back or respond to you by a certain date (e.g. after visit days), etc.). None of these answers will actually help you get in (nor will having another offer) but at least you’ll have some info.
If you have a strong sense that you might take the waitlist offer if it is made, I would just hold on until the deadline (and follow up with the waitlist). The other school knows this is a thing and will respect it. There is still more than a month to go and often waitlist movement happens at the very end.

I'm sorry to say that there aren't any programs with high acceptance rates. Maybe some are higher than others, but I'm not sure there's data and anyway, it wouldn't make for a great strategy. Any funded PhD program is bound to receive hundreds of applicants so it's really going to be a matter of finding the programs with the best fit.
I was accepted by a school that rejected me the first time. The general logic is to limit the schools you reapply to because if they rejected you once it is likelier than not that they will again. Nevertheless I reapplied to a few and one did accept me. I did not retake any exams, my WS was the same, and my transcripts were basically the same. I don't remember exactly how the LoRs were similar or not but I think at least 2 repeated. Ultimately, the only thing I changed, but changed significantly, was the SoP. I was still basically proposing to work in the same field (20th c. African American) but the first time my project was, though defined, constructed in a way that didn't make me very legible (I was combining postcolonial criticism, existential philosophy, and critical race theory while referring to early century African American lit, across French and English). My second SoP focused on a more cohesive group of authors and proposed a specific topic that was easier to pin down within the discipline. I dunno if that is helpful; for me the ilegibility of my scholarship and the difficulty of classifying it was the main thing my LoRs and I interpreted as the reason I had no success, so - given that I had a different interest I was also interested in pursuing - I just abandoned the first project entirely. Unless that's your same situation, my experience is unlikely to be helpful. My advice would be be as self-critical as you can and talk to your advisors to really pin down why you didn't get accepted (the numbers game and luck will of course be relevant, but they're unhelpful because you cannot do anything to improve them). To the degree that you can change your SoP and address those things while still being true to your interests, I would make those changes. Of course, there's always the chance that you were a borderline acceptance and making changes might push you away from acceptance, so take this with a pinch of salt.

I'm sorry to say that there aren't any programs with high acceptance rates. Maybe some are higher than others, but I'm not sure there's data and anyway, it wouldn't make for a great strategy. Any funded PhD program is bound to receive hundreds of applicants so it's really going to be a matter of finding the programs with the best fit.
I was accepted by a school that rejected me the first time. The general logic is to limit the schools you reapply to because if they rejected you once it is likelier than not that they will again. Nevertheless I reapplied to a few and one did accept me. I did not retake any exams, my WS was the same, and my transcripts were basically the same. I don't remember exactly how the LoRs were similar or not but I think at least 2 repeated. Ultimately, the only thing I changed, but changed significantly, was the SoP. I was still basically proposing to work in the same field (20th c. African American) but the first time my project was, though defined, constructed in a way that didn't make me very legible (I was combining postcolonial criticism, existential philosophy, and critical race theory while referring to early century African American lit, across French and English). My second SoP focused on a more cohesive group of authors and proposed a specific topic that was easier to pin down within the discipline. I dunno if that is helpful; for me the ilegibility of my scholarship and the difficulty of classifying it was the main thing my LoRs and I interpreted as the reason I had no success, so - given that I had a different interest I was also interested in pursuing - I just abandoned the first project entirely. Unless that's your same situation, my experience is unlikely to be helpful. My advice would be be as self-critical as you can and talk to your advisors to really pin down why you didn't get accepted (the numbers game and luck will of course be relevant, but they're unhelpful because you cannot do anything to improve them). To the degree that you can change your SoP and address those things while still being true to your interests, I would make those changes. Of course, there's always the chance that you were a borderline acceptance and making changes might push you away from acceptance, so take this with a pinch of salt.

I don't know about the acceptances rates for funded MAs but I imagine that the entry bar is a bit lower than for funded PhDs. But yes, it will probably help you to apply to places with faculty and resources that coincide with your interests. You can reach out to them but it's certainly not required.

Who gets into prestigious PhD programs? Well, I don't meant to sound flip here, but if I'm going to be completely frank ... those who get into prestigious PhD programs are, most of the time, people who went to prestigious undergrad institutions. Yes, there's a pipeline. There is nepotism. There is an attitude of "these people have what it takes to make it because they already made it--they were able to get into a prestigious school in the first place." 
Branding is powerful. Familiarity is powerful. The "benefit of the doubt" is powerful. Confirmation bias is EXTREMELY powerful. A person with a BA from University of Scranton is a bit of an unknown quantity; a person with a BA from Amherst with a connected adviser already has the bona fides and doesn't have to prove that they'll be able to pull their weight in a seminar room at Columbia. People look at the Amherst BA's writing sample with a different attitude from the one they take with the Scranton BA's. That's just basic human psychology, and no one's immune. 
I read this book a while ago, and it explains the thought process of a lot adcom members of prestigious PhD programs (and it can be rather shocking to read, tbh): https://www.insidehighered.com/news/2016/01/06/new-book-reveals-how-elite-phd-admissions-committees-review-candidates
In academia, prestige breeds prestige breeds prestige, and what you do--as either an undergrad or a grad student--is looked at through the lens of which schools you went to. That's why the faculty pipeline has remained closed to many who don't fit the elite mold. When asked why faculty continue to remain so homogenous, a professor from Penn spoke frankly: "We don't want [diverse candidates]. We don't want them": https://www.washingtonpost.com/news/grade-point/wp/2016/09/26/an-ivy-league-professor-on-why-colleges-dont-hire-more-faculty-of-color-we-dont-want-them/
Does that mean that no one from less-elite institutions can get into a prestigious school? No, of course not. We see exceptions every year. Hell, I've met many. But to be quite honest with you, they were often very, very exceptional. Just to give a rundown (and it goes without saying that this is all based on my personal anecdotal experience):
- I knew one guy who went to an unknown state school and ended up in the PhD program an at Ivy. He was extremely brilliant and hardworking and managed to publish a peer-reviewed article in a major journal by the time he was a senior in college. He also had excellent mentoring at his state school--something that is very rare in most off-the-beaten-path places where professors are less likely to be "in the research loop" (i.e. know what makes for compelling, cutting-edge research that is going to get the attention of Ivy League adcoms). 
-I knew a couple other people who managed to "trade up" from the state school where we got our master's. Neither had gone to very good undergrad institutions, but both had sky-high test scores. More importantly, both had faculty mentors who contacted faculty members at the schools to which they were applying and lobbied for them very strongly. (To give you an indication--one guy applied only to three schools, which I thought was a suicide mission at the time. But he was absolutely CERTAIN of his chances ... and sure enough, he got in to the most prestigious university in the country. Later it came out that his adviser had really pulled some strings.) 
-I know someone who started off at a community college but managed to transfer those credits to a very prestigious public university in their state. Again, they made connections at this university. Working with somewhat famous faculty, they published a paper and won a major undergrad research fellowship. They ended up getting into three Ivies. Also had sky-high (nearly perfect) test scores.
 
By contrast, most of the people I've known who went from prestigious undergrad institution to prestigious PhD institution rarely had to show the same kind of "evidence" of their brilliance. Not that they weren't brilliant--but they certainly weren't published or winning research fellowships by the time they were seniors in college. But it was accepted that they could hack it at Penn because they were already at Swarthmore, etc. 
So my main takeaway is that it's possible for people from more modest backgrounds to get into elite programs, sure. But many of those people often had to work much, much harder, score higher on those stupid tests, and make valuable connections along the way. In sum, their application package had to be near-flawless to merit serious consideration at the nation's top schools. 
Some other reading on the topic:
https://sarahkendzior.com/2015/03/06/institutional-bias-in-academia-hiring/

I think maybe you should consider your own advice (and also read the OP's post). They asked about studying at two different universities, not a dual degree. While this is technically possible, as an international student there are many loopholes one would have to jump through (here's just an example from one institution), which can make this practically unfeasible (if it is actually feasible, UMich for instance, would require part-time enrollment in both programs, which can be a tremendous roadblock for many administrative reasons). I feel like sometimes domestic students aren't fully aware of the limitations of being an international student; contrary to what another poster has said, visa status IS the foremost concern for an international student, and dismissing these concerns for incoming students can produce a lot of headaches later on (I cannot begin to describe how much bullshit you can go through as an international student doing basic things like just receiving your stipend, accepting your offer-letter employment, etc.). Of course, if you can get into a dual program then most of the concerns go out of the window because the structure is in place; but, again, this is not what OP, who was already in a PhD program, was discussing and thus is not relevant (for them, but certainly helpful for future readers).

Also I should say that as an international student, it might not be feasible. Your visa is sponsored and has limits on the amount of time you can work. While a second degree is not work, will your sponsoring dept allow you to take on this tremendous additional time commitment? Do the terms of your visa allow you to do this? I’m not sure but I’m doubtful.