One idea could be a story where a new demigod discovers they have the power to communicate with the long - forgotten minor gods and goddesses. This new ability throws the established order at Camp Half - Blood into chaos as they try to figure out if this is a good or bad thing.
Perhaps a fanfic where a demigod is cursed by a powerful goddess. The curse gives the demigod some of the goddess' powers but also makes them an outcast among their peers. The demigod then has to go on a quest to find a way to break the curse, which involves facing many challenges and making deals with other gods and goddesses along the way.
One idea could be Percy having to go on a special quest for a particular goddess that involves retrieving a lost artifact. Maybe it's an ancient weapon that was stolen by a powerful monster. Another could be Percy getting caught in the middle of a feud between two goddesses and having to find a way to make peace. He could use his unique skills and the loyalty of his friends to negotiate a truce.
A really interesting plot would be if Percy lost his memory and ended up in a mortal town. He has to figure out who he is on his own while still being hunted by some old enemies. The gods are aware of his situation but can't interfere directly because of some ancient rule. So Percy has to rely on his instincts and any small clues he can find about his past to get back to his normal self and his life at Camp Half - Blood.
Athena is also a favorite. Her wisdom and strategic mind can make for some really interesting plotlines. A fanfic could focus on a demigod who is seeking her guidance or on a conflict between Athena and another god where the demigods get caught in the middle. And her owl is a recognizable symbol that can add a nice touch to the story.
Another plot could involve Percy being tricked into taking on the role of king by a devious god who wants to use him as a puppet. Percy then has to figure out how to break free from this god's control and truly claim the throne for himself and for the good of all the demigods and mortals. He could seek the help of the wise centaur Chiron who gives him advice based on ancient knowledge.
One idea could be Percy having to go on a quest specifically for a goddess who has lost her powers. He has to travel to different realms and face new monsters to retrieve a magical item that can restore her. Another could be Percy getting caught in a love triangle between two goddesses, which causes chaos among the gods as they take sides.
In a fanfic, perhaps Percy and his friends accidentally stumble upon Medusa's lair while on a quest. But instead of immediately attacking, Medusa offers them a deal. She says she will give them a valuable clue to complete their quest if they help her get revenge on one of the minor gods who wronged her in the past. Percy and his friends then have to decide whether to trust Medusa or not.
One idea could be a crossover where the female Naruto is transported to the world of Percy Jackson. She could use her ninja skills to survive in the dangerous world filled with gods and monsters. Maybe she teams up with Percy and they exchange combat techniques, Naruto teaching Percy some of her ninja moves and Percy showing her how to use his demigod powers effectively.
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 having to face a new set of challenges in the world of the gods as a consort. Maybe he has to deal with the politics among the deities, like trying to broker peace between feuding gods. Another could be Percy using his new position to help demigods in a more powerful way, for example, getting better training facilities for them.
Perhaps Percy is chosen by the gods to be a mediator in a great council. He has to deal with the bickering and power - plays of the gods. He uses his experiences with both the mortal and divine worlds to bring some order. Along the way, he uncovers secrets about the gods' past that could change his relationship with them forever.