To my knowledge, all of the Ivy League universities (in addition to Stanford) recommend or require two SAT subject tests. Georgetown, which is not an Ivy League institution, is the exception; it requires three.
Putting aside Georgetown, is there any upside to taking three SAT II’s, though? For example, if somebody is planning on taking the Math Level 2 and U.S. History tests, would the Ivies or Stanford look more favorably upon them if they submitted three scores (so, Math Level 2 and U.S. History, as well as an additional one in Literature), as opposed to two? In other words, would three tests (instead of two) give a candidate more of an edge (assuming they scored well on all three)?