Ivy League + SAT Subject Tests

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)?