CSS allows an HTML element to have multiple classes:
Nibbles
But is there a limit
No. I don't think, I have ever come across any such limit/
EDIT: Sorry for the casual remark.
According to the specifications, there isn't any limit but someone has tried to reach this limit and it seems the limit for Opera, Safari supported well over 4000 classes, and Firefox at least 2000 classes!
Source: http://kilianvalkhof.com/2008/css-xhtml/maximum-number-of-supported-classes-per-element/