My twins are sophomores in college. They applied to an overlapping list of colleges but ended up at different ones, which is just as well as they are very competitive. And I have already verified that they will not graduate on the same weekend. 
Just an FYI, don’t let the price tag of top private colleges automatically scare you off. Colleges that meet need will take into consideration the multiple children in college and your overall financial situation, and they can end up being much more affordable than state schools (depends on the state, of course - I am in a state with expensive public universities).