I'll give you Eternal Sunshine, but that's it. Perhaps Man on the Moon, as well, but only as a technicality because he was playing Andy Kaufman. Overall though, while he has toned down his act a bit since his initial run of success -- Dumb & Dumber, Ace Ventura, The Mask -- the majority of his roles are still all cut from the same cloth. Just because the sophomoric overtones are gone, doesn't mean that he has actually added any depth to his roles; they are still all rooted in phsyical comedy and wackiness. The movies you listed do nothing short of supporting this. You would've done much better to have listed stuff like Truman Show and The Majestic. Three movies, however, are hardly enough to break the mold he's already set for himself.
Like I just said with Carrey and three movies which stray from his copy-and-paste style, it takes a lot more than making one "serious" movie to get the general public to view you as something other than one certain type of actor.

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