One possible plot could be that Percy jumps off Olympus in a moment of extreme despair. Maybe he feels betrayed by the gods and their constant manipulation. He jumps, thinking it's an escape, but then discovers he has new powers or a new mission on earth. For example, he might land in a mortal city and realize he has to protect it from a new threat that the gods are ignoring.
Well, perhaps in the fanfiction, Percy jumps off Olympus as a form of protest. He's tired of the Olympian hierarchy and their lack of care for demigods. After jumping, he could end up in a hidden realm. There, he meets old friends or enemies who have also been exiled. Together, they form a group to try and change the relationship between the gods and demigods from outside Olympus.
In this 'percy jumped off olympus' fanfiction, it could start with Percy being fed up with the politics on Olympus. He jumps off and lands in a strange place. This place could be a magical forest that has its own set of rules and creatures. Percy has to learn to survive there while also dealing with his inner turmoil. He might start to question his own identity as a demigod and his place in the world, and eventually find a new purpose that is different from what the gods had planned for him.
Annabeth could be a main character. She might be desperately trying to find Percy after he jumps off Olympus. She could use her wisdom and strategic skills to track him down, facing various obstacles along the way, like mythical beasts or other unfriendly demigods. Another character could be Grover. He could sense Percy's distress and join Annabeth in the search, using his nature - related powers to help them.
Perhaps the plot involves Percy using his new princely powers to bring about positive changes in Olympus. He could work on improving relations between the gods and demigods, for example. Since he has always been a bit of an outsider among the demigods because of his unique abilities, this new role could give him the opportunity to bridge the gap between the two groups. He may also have to face some sort of conspiracy within Olympus that threatens his position as prince.
In this fanfiction, perhaps Percy is influenced by some dark force. This force convinces him that the Olympians are corrupt and need to be overthrown. He then betrays them by stealing important artifacts from Olympus that are crucial for its protection. He might also try to turn the demigods against the Olympians.
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.
Well, it could be about Percy facing a new and powerful enemy that threatens Olympus. He might have to gather different demigods from various cabins to form a united army. Maybe there are some internal disputes within the army that he has to resolve as well.
It could be about their unique upbringing on Olympus. Maybe they have to deal with the politics among the gods while growing up. For example, Percy might struggle with Poseidon's expectations and his own identity in this divine setting. Jason could be learning about his Roman heritage in a more Greek - influenced environment. And Nico might be trying to find his place among the living and the dead while being raised on Olympus.
Well, one possibility could be that they are given special status on Olympus. Maybe they are tasked with keeping the peace among the gods, which would lead to a lot of interesting interactions with the deities. They might also use their unique powers to improve the living conditions on Olympus, like Percy controlling water to create beautiful fountains or something.
Perhaps in this fanfic, Percy is raised as a sort of prince on Olympus. He could be given tasks by the gods to prove his worthiness to be among them. This might include going on quests that are not just for the safety of the mortal world, but also for the stability of Olympus itself. He would also have to navigate the complex social hierarchies among the various gods and goddesses.
A possible plot twist could be that one of them is actually a secret weapon of an enemy god. For example, Nico could be unknowingly influenced by a dark force that wants to use his powers to bring chaos to Olympus.
One possible plot development could be Percy and his friends facing a new, even more powerful enemy. Maybe an ancient primordial being that was previously sealed away has been awakened. For example, a new Titan or a primordial chaos entity. Another development could be Percy exploring his new powers or abilities that he might have gained after the events of Heroes of Olympus. He could be training other demigods as well, passing on his knowledge and skills.