CSS allows an HTML element to have multiple classes:
Nibbles
But is there a limit
There is no technical limit (barring the amount of memory the browser may be consuming), but one should heavily consider having loads of classes on any element as the browser will have to parse all the classes, apply those styles and render the page.
Also, if you need to search the DOM for elements of a particular class and elements contain loads of classes, you may likely see a performance issue if the JavaScript interpreter has to parse loads of classes.