Well, that depends on a couple of things. First, how you state it in your contract, and second, how nice do you want to be.
If it snows 3-inches, you plow, and it snows another 2-inches, YES by all means I would charge. If it was juist to go back and get rid of the windrow that the city truck left in front of the driveway, you may not want to collect on that one. But I have heard of some people that include a small charge into their contracts for going back to do a cleanup. This is especially popular when the account is somewhat of a far dirve. This way you at least get some money for gas out of it.
If you are referring to the specs in an already written contract or bid, per push means each time you clear the lot. So if you need to clear that lot 3 times during a particular storm, the charge would be 3 times the per push price.
"or the total snow fall no matter how many visits." - this is considered by the inch (or increments of inches, 1"-3", over 3" - 6", etc.) So in that case if the over 3" - 6" price is $500.00 and you neede to plow it 3 times for a 5.5" storm, the charge is $500.00. If you plowed that same storm twice instead, the charge is $500.00.
In the long term, if you do your homework, you'll come out better with seasonal contracts.
You need to know:
weather patterns in your area,
weather history in your area (20 years)
your all-found costs and overheads,
and your productivity/mechanical availability with your equipment.
If you get a handle on all of these, you will be sucessful without ever having to get the tape measure out.