28
You can count past 1,000 on your fingers by using binary, instead of just 10
(www.mathsisfun.com)
Depending on how well you can control your individual joints, could get base 3 or 4 going.
Binary instead of unary
I just tried, and counting this way on one's fingers is not very useful because its awkward. Try counting to 32 and tell me if you didn't experience frustration bending your fingers.