But obviously "the sequel is a completely different genre" is not something studios tend to go for.

Yeah, the only one I can think of that did that was Chronicles of Riddick and that... did not go well.

Alien to Aliens? That one went pretty well.

Of course, the other immediate example I can think of is The Matrix/The Matrix Reloaded (action movies) leading into The Matrix Revolutions (war movie) and that went about as well as Chronicles of Riddick, so. :)