Techincally you can hold on to more than one acceptance. However at some point each school that you are accepted at will require you to put down a deposit to remain on their accepted list. If you don't pay the deposit they will assume you don't want to go to their school and will drop your name.
So if you get accepted at 3 schools, each school will ask for a deposit, the amount of which is different for any school. My school, Oklahoma, wasn't too much ($100), but I've heard of some schools being $1000 and up.
Therefore if you want to hold on to each of those 3 different acceptances, you can do so by paying each deposit. But it might cost you around $3000 to do so, and since you can only go to one school, that would be $2000 down the drain.
Anyway, this is how I think it's done. If I'm wrong or if there are schools with exceptions, someone else can correct me.