Adding clubs such as theatre club science club e.t.c.

One way to spice it up, is to add things that are possible in a monster school but not done in a normal school, add a weird club such as a prank club, where the leader is the one with the most pranks.

Also since this is a school based game, DEFINITELY ADD BULLIES, they will spice up the gameplay in ways you can't imagine.

Depending on the vibe you are going for

Maybe Tag or hide and seek with the linvisble man or maybe he is creeping on someone. 

Someone put garlic in food in the cantine and it is making the Vamp kids sick

Basketball against werewolfs

The werewolf guys or gals are clocking up the pipes in the sinks and toilets with all their shedding.

If the other characters  can date eachother maybe you can help or sabotage their relationships.

Maybe the AV club have problems with the fact that Vamps don't show up on camera

And definately bullies and some great and awful teachers could also add a lot

Battle of the Bands in this setting alone could be its own (admittedly very small) game. Think of horns and horns. Blowing toxic gas (into what?). Electricity. Drums.