To answer your first question, I have not heard of a program providing any leeway on paying the deposit to secure your seat for the next cohort. The reason why programs have deposits is so they can be assured, up to a point, that they have a full class and are not scrambling to extend an acceptance at the last minute and to reasonably cover any costs associated with having to pull from a waitlist or interview more candidates.
The answer to your second question is, of course. It is called a non-refundable deposit. You cannot be forced to attend a program if you choose not to. You will just forfeit your non-refundable deposit if you choose to do so. An aside to that, I wouldn't be surprised if some programs have a clause in their acceptance package that asks you to withdraw yourself from consideration to any remaining programs you're waiting to hear from.
All in all, considering how competitive it is to gain acceptance to these programs, I'd consider yourself very lucky if you find yourself in a position where you are waiting to interview at multiple schools with an acceptance in your back pocket. I wish you the best of luck with the interview you do have. I, myself, am still waiting on my applications and hope to get an interview somewhere.