The bank I'm with at the moment allows me to create new accounts on the fly in addition to the traditional checking/savings. I've never created more than one PayPal (and keep in mind that doing so without PayPal's knowledge probably puts you at risk of having your money frozen), but the uniqueness of a bank account is likely determined by its account number, so using alternate accounts should work just like using checking and savings separately works. Phone your bank and see if this is something you're able to do.
Better yet, doesn't PayPal have processes to remove limits? Why not just do it through PayPal?