I've never heard of not being allowed more than your number on your roster....just never over at any one time.
I think if you do this though, it really needs to be stressed to the parents that they can NOT be late as it puts you at risk for being shut down or fined. I wouldn't even bother with a late fee in this situation, it would be late once they are termed as you can't take that risk. Give 30 minutes in between just in case though and you should be fine!