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To take this from last to first: 1) You cannot necessarily assume that a top-40 PhD puts you in a position to get an R2 tenure-track job. The job market is increasingly competitive. A colleague of mine at an R2 was on their department's search committee this year. They got over 200 applications. A lot of them were advanced assistant professors now taking advantage of the fact that the job market is less terrible than any time since 2009 to move or negotiate outside offers. He mentioned a few names to me that I was very surprised to hear, including an assistant with over 1,000 citations already (you'd know their name if you studied the topic; one book, multiple top-three journal articles, several articles). Files also included recent PhDs/ABDs from top-10 schools. The department ultimately offered the position to a top-40 ABD for a host of reasons, but you cannot assume this is a normal outcome. 2) Is the graduate department known for what you study? If you know any, ask other R1 professors or those who have a good publishing record about the program's reputation. Perhaps ask your letter writers. If not, seek out recent PhDs from the program in your subfield and ask how happy they were with the training and preparation they received. On this point, a "top-40" program may not be known as such in your specific area. It could be top-25 or top-60, for example. I got my MA at a top-50 place that wasn't known for my subfield, and my PhD at a top-15 place that specialized in it. The difference was greater than the 35 places implied by looking at US News. Probably the best example of subfield variation in rankings is Stony Brook. It ranks in the high 30s, but if you do political psychology, it's a top-five program. 3) The decision to improve your file and apply next year depends on your risk tolerance and your assessment of how much you can improve it. If you need to do something relatively simple like improve your GRE score, then it may be worth it. If it is taking a year to critically review the major literature in your subfield to better articulate your research interests and fit, then probably less so. People do this, but it's what you'd be doing in the field seminar your first year of grad school. If you can stomach it, email the DGS at places you were rejected and get their feedback about why they rejected you. If their assessment seems nonspecific, then you have to at least think about the possibility that your letters were weak, which they cannot tell you anything about, legally. This is probably not the case, given four acceptances, but it is possible. 4) You have the option of transferring after a year or two in graduate school. This requires some sensitivity. Your professors—especially if they are senior—can be out of touch with your subfield and the discipline, and may have an inflated sense of their own place in it. If you can broach the subject diplomatically, great. If now, try to get letters from junior faculty who are up on the latest developments and realize how competitive the job market has become. I avoided this situation when I transferred by getting a letter from a professor I worked closely with in my second field, which I added to two of my undergraduate letter writers. An example of how senior professors can be delusional: a top-25 program that was about as strong across subfields tried recruiting a member of my PhD cohort who had an offer from a CHYMPS school. A senior faculty member in his subfield said their faculty was on par with the CHYMPS program, citing the losses of senior professors who had left 10 and 15 years ago.