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FizzyShellfish - yeah, it does that. The main quest is deadly serious (or maybe I should say "main quests" - each character has his own). The side quests are mostly for laughs.
I remember the first few hours being pretty confusing (and having an awful time figuring out that you save the game by going to a phone booth) but, once I got a handle on who's who, it got really fun.
The beat-m-up is the battle system. That expands a lot into 6 different styles (3 per main character).