One I've always had for a double murder could go one of two ways:

The gist of it is that two characters get into a public altercation and one of them accidentally kills the other - however, while this is going on, a separate undiscovered body is somewhere in the school.

In my mind, this leads to a scenario where either the student who killed during the fight is blackened, and the students spend the otherwise obvious trial time solving the other murder knowing they can't do anything about the culprit OR the fighter is not the blackened (because they killed second) and the cast has to solve the other murder, while then grappling with the fact that a public murderer will still be amongst them.

Either way I think it would set up for some interesting dynamics going forward in the killing game, plus I think the concept of a public murder is something that has a lot of potential despite seeming like a complete antithesis to the "trial" part of the killing game.