To my knowledge, all of the Ivy League universities (in addition to Stanford) require two subject tests. (Georgetown, a non-Ivy school, is the outlier, as it asks for three.) Putting aside Georgetown, is there any reason to take three tests instead of two? Like, if somebody is planning on taking Math Level 2 and U.S. History tests, would a third test (say, in Literature) improve their prospects (even slightly)? In other words, would Ivies that ask for two tests give weight to the third one and be impressed by somebody going above and beyond?
You only have to submit two unless a school requires all tests (Stanford?) so some students may be better taking three and sending the best two scores.
@Sportsman88: Thank you for the feedback. I just wanted to make sure that taking two tests (and doing well on them) wouldn’t be seen as bad for Ivies in comparison to somebody who has taken three (and done well on them). Am I correct in assuming that isn’t the case if the school asks for two?
If the school asks for 2 (and FYI, for most Ivy League schools, they are recommended, but not required), they will look at the top 2 scores. In absolutely no instance will a school go “Oooooh, this kid showed initiative by taking 3.” Also, as an FYI, At my college, little elves in the basement (well, work/study students) assemble a cover sheet which lists only the top scores; the other scores will appear further inside the package if the AO decides to dig for them.
Any two subject tests should suffice, unless the student is applying to a special program which has its own requirements. For example, some of the BS/MD programs require Math 2 and Chem, and some Engineering programs require a Math and Science. Absent that, any two should do the job.
I was always under the impression that Ivies would look down upon somebody who didn’t take both a math and science SAT II. Am I incorrect in assuming that? Like, if somebody is a political science or economics or finance/business applicant, there isn’t an implicit bias against them if they don’t take a science SAT II, right? (I know that such an expectation/requirement is typically set for science/engineering/premed students.)
I was told by a few people “in the business” that there are some colleges, not necessarily Ivies, that like to see a student who can perform well in both math/science and non-math/science subject tests, such as a Math II and Literature. Some want to see a more well-rounded candidate. Obviously, not Cal Tech, MIT, etc.
@sushiritto That makes sense. Just wanted to make sure that an HYPS applicant wouldn’t be penalized for taking Math Level 2, U.S. History, and Literature (and no science tests).
I spoke to a Harvard interviewer. And I spoke to a test prep company executive. The only reason I would take a 3rd subject test is if would like to see which two subjects tests have the highest scores and submit those two. Or you’re applying to Georgetown. And you have the time and energy.
Otherwise, one from math/science and one from non-math science works fine for most schools, even for STEM majors in many circumstances. It shows “versatility”, assuming you do well at both, of course. 
@sushiritto When you say “non-math science,” you mean neither math nor science (so English literature, U.S. or world history, or a language), right? So, someone taking Math Level 2, U.S. History, and Literature wouldn’t be looked down upon if they do well.
Yes, you are incorrect in your assumption. Unless the college wants something specific (like Penn engineering wants a math and a science), then it’s your choice. Colleges do not expect applicants to read the tea leaves. If they want something specific, they will tell you.
@XCX0501 That’s correct.