I can't imagine what type of request Depp agent has to screen through, and further still how they decide what crazy roles Depp is willing to take on.
Of course, not every role is absolutely over the top, there's no doubt Depp has range. Early on in the year there definitely seemed like Depp might get Academy Award recognition for Public Enemies playing John Dillinger, but precursor's, even the Golden Globes (8 nominations in lifetime) have passed up this performance.
Johnny Depp's previous three Oscar nominations have all been from this decade and include his performances in Finding Neverland, Pirates of the Caribbean: The Curse of the Black Pearl, and Sweeney Todd.
Next year Depp has at least two prestige performances, one as the over the top Mad Hatter in Tim Burton's Alice in Wonderland. And while Depp is sure to enchant in this role, I would assume the over the top performance probably isn't his Oscar gem (but of course, one would have thought the same thing initially of his Jack Sparrow creation for Pirates of the Caribbean.)
Depp also has a role in the film the Rum Diary, a long discussed film adaptation of the Hunter S. Thompson's The Rum Diary, where Depp stars as a journalist in the late 1950s who tires of American life and moves to Puerto Rico to write for the San Juan Star newspaper. There he chases women and soaks himself in alcohol.
Could this be Depp's 4th Oscar role?
Maybe, but I get the sense that Depp really doesn't care. His choices and performances lead me to believe he does his own thing and isn't really that concerned with appealing to the critics, but instead creating great characters.