I think Eddie Murphy would have been capable of a serious dramatic role had he not started doing Nutty Professor and Dr. Doolittle type movies after he had kids. In his early movies he does a good job of playing serious while being funny on the side.

A lot of comedic actors are all or nothing when it comes to serious acting, but he balances it pretty well in movies like 48 Hours and Golden Child. Not that those movies are shining beacons of cinematic prowess, but I think they show he is capable of being a serious actor.

Coming to America is another good example. While it's undoubtedly a comedy, he shows that he is capable of playing something different than the sleazy con artist/rogue cop character he played in his earlier movies.

Unfortunately he switched to kid movies, so we'll likely never see if he is capable of pulling off an Eternal Sunshine-style transition. Bill Murray is a good parallel because he also started on SNL and played a lot of silly (yet well done) roles as well as kid movies like live action Garfield before switching to more serious stuff like Lost in Translation.