“I was just found guilty of running FOUR consecutive red lights in NYC. My fine is $2000. If I don’t pay the balance shortly my license will be suspended. Is there a maximum number of red light violations that I can be liable for? I’m hoping to get just one dismissed after the fact - that would be a great relief.”

Yes, there is a maximum number of red violations for which you can be held liable: you cannot be held liable for any more red light violations than you actually commit.

Recommended reading (click on the picture for details):
How to Fight Your Traffic Ticket and Win!: 206 Tips Tricks and Techniques