There are a few people who have made that transition, or kind of ventured out into it. The most interesting ones to me so far have been Jim Carrey and Robin Williams. Both rather silly and over-the-top in their comedic approach, but both have managed to tone it down for different parts, or make movies that actually have more than just site gags and laughs.

Bill Murray has already struck me as someone wth a serious side, but wants to hide, for whatever reasons, behind the comedy.