One idea could be to write about Michael's backstory before arriving at Hazbin Hotel. Maybe he had a difficult life on Earth that led to his damnation. You could explore his relationships, like if he had a family or friends that he left behind.
You could also write a fanfiction where Michael discovers a hidden power or ability within himself while at the Hazbin Hotel. This newfound power could change his role in the hotel and how others perceive him, leading to a whole new set of adventures and challenges.
The 'Mysterious Past' trope is also common. Since not much is known about Michael in the original Hazbin Hotel concept, fanfiction writers like to fill in the blanks with all kinds of secrets and past traumas that shaped him.
One idea could be that Bill Cipher somehow ends up in the Hazbin Hotel universe. Maybe he's there to cause chaos among the sinners. He could start by tricking some of the characters into making bad deals, like he did in Gravity Falls.
You could also write a fanfiction about a new character arriving at the Hazbin Hotel. This new character could have a unique power or a very different personality from the existing ones, which would create all sorts of new interactions and storylines. Maybe they have a special ability to see the pasts of the other characters and use that to help them on their path to redemption.
One idea could be exploring the backstories of the characters in more depth. For example, delving into how Alastor became the Radio Demon. Another could be creating a new character who arrives at the hotel and causes a stir among the existing residents. Maybe a character from a different dimension or with a very unique power.
One idea could be a story where Lucifer and Alastor have to team up to deal with a new threat to Hell. Maybe a powerful demon from another realm is trying to take over, and they have to put aside their differences. They could start off not trusting each other much, but as they face challenges together, they begin to respect one another's abilities.
One idea could be exploring Lucifer's past before ruling Hell in the Hazbin Hotel universe. Maybe his rise to power, his relationships with other powerful entities at that time.
One idea could be that the characters from Hazbin Hotel end up in Paris where the Miraculous Ladybug story takes place. They could interact with Ladybug and Chat Noir, and maybe some of the chaotic energy from Hazbin Hotel causes trouble for the heroes as they try to keep the city safe. For example, Angel Dust might accidentally cause a distraction during an akuma attack.
Another option is a crossover with Gravity Falls. Dipper and Mabel could end up in Hell for some wild reason, like following a strange portal. They'd meet the Hazbin Hotel crew and chaos would ensue. Dipper would be all about trying to figure out the logic and secrets of this new place, while Mabel would probably befriend some of the more outlandish demons or sinners. Charlie would see the Pines twins as a chance to prove that redemption is possible even for those from other dimensions.
It also keeps the interest alive during the wait for new official content. When there's a long gap between new episodes or developments in the official Hazbin Hotel story, these fanfictions give fans something to enjoy. They can explore new storylines and ideas that are inspired by the original but still have their own unique twists, like a fanfic where the characters react to a time - travel scenario.
One idea could be Adam's backstory exploration. Maybe he had a different life before coming to the Hazbin Hotel universe and that could be delved into. For example, his family, his upbringing, and how those things might have shaped his current self.