Theme a multichoice node

I'm attempting to theme a Quiz, with multiple choice questions. For the initial Quiz node (where "Start Quiz" button is), the node has a class of "content-type-node-quiz". However, once you start taking the quiz there is no node class associated with a multiple choice question. The only class available is "region-content" or "region-content-inner", which is to broad of a class (it impacts other areas of the site where the desired style is not wanted).

Is there a way to add a "content-type-node-quiz-multichoice" class to this type of node? Or how I would otherwise theme it without impacting other nodes in the same region?