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Is it possible to re-neg on a first deposit if an acceptance comes after the deposit date to another school? Is the second deposit the one that is really binding?

Deposits aren't binding. Some schools will be unhappy if you cross deposit (deposit at 2 schools at the same time). Some will ask that you withdraw from other schools (I think Penn did this when accepting their scholarship offers). But in general, no deposit is binding. If you get in off a waitlist later you are free to switch.