A possible plot could be that there is a prophecy in both worlds that only a combined force of demigods and elves can stop a great evil. So, characters from both universes are brought together. They have to overcome their differences in culture and abilities. The elves might find the demigods' fighting style too rough, while the demigods might think the elves are too secretive. But in the end, they work together and use their unique powers to defeat the evil.
Another idea is that Sophie Foster from KotLC travels to the Percy Jackson universe. She could be mistaken for a demigod at first. She would have to learn about the Greek gods and monsters. Her telepathic abilities would be really useful in the Percy Jackson world. For example, she could communicate with some of the monsters to find out their plans. And Percy and his friends would help her understand this new and dangerous world.
Fitz and Grover could also have a unique interaction. Grover is very in - touch with nature and has his own kind of "sixth sense" for danger. Fitz, being an elf, also has a connection to nature in his own world. They could bond over their love for nature. Grover could introduce Fitz to some of the Greek nature spirits, and Fitz could show Grover some of the beautiful and magical places in the elven world. They might also have some comical moments when they try to understand each other's languages and customs.
One idea could be that Naruto, with his powerful chakra and skills, is somehow transported to the world of Percy Jackson. He might be mistaken for a demigod because of his extraordinary abilities. Naruto could then team up with Percy to fight against a common enemy, like an ancient monster that threatens both their worlds.
Another way to do this crossover is to have a prophecy that links Percy and Thor. The prophecy could say that only by the combined might of the son of Poseidon and the God of Thunder can a great evil be stopped. This evil could be a new kind of monster that has the ability to absorb both Greek and Norse magic. Percy and Thor would have to overcome their differences quickly. They would travel to different realms, both Greek and Norse, to gather items or allies needed to defeat this monster. Along the way, they would face many challenges and grow to respect each other.
A third idea is a role - reversal type of story. The demigods from Percy Jackson end up in the world of Fire Emblem Awakening. Percy could use his water - based powers in a unique way in the battles of Fire Emblem. Annabeth could use her strategic mind to help the Fire Emblem characters plan their battles better, and they all work together to defend the kingdoms in Fire Emblem Awakening from an invasion.
One idea could be a crossover with the Harry Potter universe. Percy could visit Hogwarts and have to deal with both magical and mythological threats. Maybe he'd team up with Harry to defeat a common enemy that combines dark magic and ancient Greek monsters.
Another possibility is that Percy somehow gets transported to Eragon's world. He has to adapt to the new environment and figure out how his demigod powers work there. Eragon could initially be suspicious of Percy but then they realize they can help each other. Percy could teach Eragon about water magic, which is new in Eragon's world, and Eragon could show Percy how to ride a dragon, which would be an amazing experience for Percy.
One idea could be that Percy ends up in the Underground world of Undertale. He might use his water powers in unique ways against the monsters there. For example, he could create water shields to block attacks from the more aggressive monsters like Undertale's Flowey. Another idea is that Sans could somehow end up in the Camp Half - Blood from Percy Jackson. Sans' laid - back attitude would be a contrast to the usually intense and heroic demigods at the camp.
One interesting idea could be the crossover of Percy Jackson with other mythologies in a unique way in the fanfiction. For example, combining the Greek mythology elements from Percy Jackson with Norse mythology. This can create new and exciting adventures for the characters. Another aspect could be exploring different character relationships in a fresh light. Maybe seeing how Percy would interact with characters from another fictional universe in a situation that tests their loyalties and abilities.
One idea could be that Percy and his friends get transported into an anime world like Naruto's. Percy could use his water powers in the deserts of Suna and have epic battles against the sand ninjas. They might also learn new skills from the Naruto characters, like chakra control, and in return, teach them about Greek mythology.
A crossover with Harry Potter could be cool too. Percy could visit Hogwarts and participate in a Triwizard Tournament - like event. He'd be the outsider with his unique demigod powers, and there could be a lot of fun interactions between him and the Hogwarts students, like Hermione being intrigued by his abilities.