One idea could be exploring the backstories of the minor characters. For example, you could write about how a particular student ended up at Heavenly Host Elementary in the first place. Another idea is to create an alternate ending where the characters manage to escape the horrors of the school in a different way than in the original. Maybe they find a hidden passage that leads them directly out, but it has its own set of challenges.
A cool concept for a Corpse Party fanfic could be a time - travel story. Imagine a character somehow going back in time to before the events at Heavenly Host Elementary. They could then try to prevent the initial tragedy that led to the school becoming haunted, like stopping the earthquake that killed all those students in the first place.