In response to the Ranma/Red Dwarf Crossover idea:

Another way one could go with that was to have Ranma zap from the Takahashi
Reality into that Red Dewarf alternate realty where women and men have
reversed roles.  And just have Ranma have to readjust to how to behave as a
part of both genders.  Could be either with reverse gendered Nermians or
people from Lister's time.