Perhaps the story involves Percy being framed as an assassin of Olympus. He then has to clear his name while dealing with the real assassin who is causing chaos among the gods and demigods. The plot might also include Percy's journey to discover who set him up and why.
It could be a new demigod who has a grudge against the Olympians. This demigod might be using Percy as a tool to carry out their assassination plans.
It's not likely that the actual Olympus (in the context of the Percy Jackson series being a place of the gods) reads fanfiction. Fanfiction is a creation of the fans in our world, and there's no indication in the books that the gods or Olympus as an entity would engage with it.
One idea could be Percy having to face a new, unknown monster that is immune to water. He'd have to rely on his other skills and the help of his friends in a completely different way.
Well, in many fanfictions, Percy might be on a mission to assassinate some powerful being in Tartarus. Maybe he has to face all kinds of hellish creatures and overcome insane challenges. It could involve him using his water powers in unique ways, like creating weapons out of water to fight the demons of Tartarus.
Well, you could write a fanfiction where a minor character from the original 'Percy Jackson and the Blood of Olympus' gets their own story arc. Maybe a character who was always in the background but had a lot of potential. For instance, a demigod who discovers a new power related to the blood of Olympus that was previously unknown. They could then go on a journey to master this power and in the process, uncover secrets about the Olympians that were long forgotten.
One idea could be exploring a new prophecy that involves Percy and his friends having to team up with some of the lesser - known gods. This would introduce new characters and powers into the story.
One idea could be Percy discovers a new, hidden power within himself that is linked to an ancient prophecy. Maybe he can control the elements in a way no demigod has before.
One interesting plot twist could be that the Staff of Olympus has a hidden power that no one expected. For example, it might be able to reverse time in a small area, which changes the whole dynamic of a battle. Another could be that a character who was thought to be an enemy turns out to be a key ally in the quest related to the Staff. Maybe they were under a spell or had a secret mission all along.
A plot where the demigods have to team up with their mortal enemies, like some of the monsters, in order to face a greater threat that endangers both their worlds. This could lead to some really interesting character dynamics and moral dilemmas.
One idea could be exploring the relationships between the demigods in more depth. For example, how Percy and Annabeth's relationship evolves after the events of 'Blood of Olympus'. Another could be creating a new adventure for the demigods that involves a forgotten prophecy. Maybe they have to travel to a new, unknown part of the mythological world to fulfill it.