This may not be exactly on target because I am not completely clear on what you want to do. However, assuming you mean you want to assign a different class to a div in response to an event, the answer is yes, you can certainly do this with jQuery. I am only a jQuery beginner, but I have used the following in my code:
$(document).ready(function() {
$("#someElementID").click(function() { // this is your event
$("#divID").addClass("second"); // here your adding the new class
);}
);}
If you wanted to replace the first class with the second class, I believe you would use removeClass first and then addClass as I did above. toggleClass may also be worth a look. The jQuery documentation is well written for these type of changes, with examples.
Someone else my have a better option, but I hope that helps!