My genre categories may not line up with everyone's, but:
Robert Wise did historical drama, disaster, musical, horror, thriller, war, science fiction, and crime. I can't think of a comedy off hand.
Robert Altman did period drama, contemporary drama, fantasy, comedy, thriller, mystery, science fiction, musical, western and crime.
John Ford did period drama, biopic, current-event drama, documentary, war, romance and of course western. Borderline on comedy and mystery and no real musical but there was so much song and dance in Ford movies that one critic said they felt like long trailers for imaginary musicals.