jdsj

Don't feed the trolls, people.

Don't feed the trolls, people.

Don't feed the trolls, people.

there's a current thread on this board about moving expenses:
 

Some of these answers may be really field dependent.
 
If you appear like you are simply going to go to the school that pays you more, both schools will be put off by this. On the other hand, if you demonstrate that you need the additional stipend in order to make ends meet then they will at least understand why you are asking for more (even if they can't offer it).
 
From your description, it actually does not sound like you are in any position to negotiate at all. Usually, you do this if you really want to attend School A, but School B has a better financial offer, and that School A and School B are both similarly ranked programs. Then, you can tell School A that you really prefer their program but School B is offering such-and-such and they are also a good program and having financial security etc. would be better for you there. Then you would ask politely if they were able to offer more.
 
Strictly speaking, I do not think it's unethical to pit two schools in a bidding war. That is, in the above example, if you really wanted to attend School B (secretly) but you tell School A the above and then you get an offer from School A that is better than B. Then you would go and tell B that A is offering such-and-such and try to get a better offer from B. I don't think this is unethical, but I really really doubt it will work in practice. And even if it's ethical, School A is going to be pretty pissed at you because they likely went through a lot of trouble to authorize the better offer. So the reality is that graduate students don't really have a lot of ability to negotiate and I think you have to weigh the practical aspects too. I think that trying to pit two schools against each other has a low chance of working and a high chance of pissing everyone off. So I would advise against that.
 
Instead, I would advise for honesty and good faith in your negotiating. That is, only ask the school you are actually intending you attend to raise their offer. That is, be prepared to accept their offer if they agree to your request. And if they don't (or only go partway), then it's up to you to decide between A and B. 
 
Stipend is certainly negotiable, but it can be pretty tough at some places. You will likely get an answer like "we pay all our students the same". This may actually be an outright lie to discourage negotiation but it's also often true. However, they can always say things like that which makes it very hard to gain ground on that front.
 
So, here are some other financial things that people in my field often negotiate outside of stipend:
 
1. Increased support for health insurance (if it's not already fully covered). Ditto for any spouse and/or dependents you may have.
2. Relocation costs. In my field, most postdocs positions will cover between $1000-$3000 in costs, so start there but be prepared for a smaller number for grad students.
3. Work-related travel expenses. Get a promise from your supervisor to send you to X conferences, or a promise from a department for a travel grant of $X (need to get this in writing).
4. Research grant expenses. One program at my current school gives every student a $1500 grant to buy things (many use this to buy a laptop but you can also use it for travel) etc.
5. Increased TA assignments (more work for more money)
 
You can also ask for non-financial things that might make your life easier:
 
1. Switch out TA work for RA work. (Might be field dependent, but our RA work is just work towards dissertation, so this effectively reduces  your TA obligation while keeping the same pay--but make sure TA and RAships are awarded the same way).
2. Ask if you can get priority in whatever waitlists that might be relevant to you: e.g. housing, childcare, etc.
3. Ask nicely if you can get some upgrades for your office (only applicable if you already visited and know what your space will be like)--e.g. one school installed a new bulletin board at my request and also found a better chair and filing cabinet for me. However, this is something that doesn't really make sense to get in writing or as a condition of your acceptance. Instead, this is something you might ask your supervisor if it is relevant or comes up. For my example, the prof actually asked me what I would want, so that was a nice opening for me to just give a wishlist. I don't know if it's that easy if ask for it upfront though.
4. Guaranteed vacation time (especially if you need to take time off for something you know is coming up, e.g. wedding)
 
Just some ideas that you can try to ask politely for. Don't be surprised if they say no. But you have nothing to lose if you approach this in an appropriate way.

I do not believe applying to more schools is going to help at all.  Having 5 very strong, tailored applications to specific programs increase your odds drastically.  10-13 applications are bound to be weak because you cannot possibly spend as much time on them as is needed.
 
I only applied to 3 programs and have been accepted to each with funding.

I do not believe applying to more schools is going to help at all.  Having 5 very strong, tailored applications to specific programs increase your odds drastically.  10-13 applications are bound to be weak because you cannot possibly spend as much time on them as is needed.
 
I only applied to 3 programs and have been accepted to each with funding.

I do not believe applying to more schools is going to help at all.  Having 5 very strong, tailored applications to specific programs increase your odds drastically.  10-13 applications are bound to be weak because you cannot possibly spend as much time on them as is needed.
 
I only applied to 3 programs and have been accepted to each with funding.