Well, one idea for this crossover could be that Savitar somehow ends up in the world of Percy Jackson. Maybe he's chasing after some new kind of speed - the speed of a demigod? And Percy has to figure out how to deal with this strange, super - fast being who doesn't seem to follow the normal rules of the Greek myth world.
Another theme is friendship and teamwork across different universes. When Percy teams up with characters from other fictional worlds, they have to learn to trust and work together. This shows how different characters with diverse backgrounds can come together for a common goal, like saving both their own worlds and the ones they've crossed over into.
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.
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 one to check out is 'Justice League meets Camp Half - Blood'. In this fanfic, the Justice League discovers Camp Half - Blood. It's cool to see how Batman would interact with Chiron, or how Wonder Woman would view the demigod powers. There are a lot of great character moments as the two very different universes collide.
One great Percy Jackson crossover fanfiction is the one where he crosses over with the Harry Potter universe. It's exciting to see how the magic of the two worlds interact and how Percy and Harry might team up. Another good one is the crossover with the Avengers. Imagining Percy fighting alongside superheroes like Thor and Captain America is really cool.
Another theme is the idea of a shared threat. Since both Percy and Harry are heroes in their own right, a lot of crossover fics will have them face a danger that neither could handle alone. This could be a new dark force that combines the worst of the magical and demigod worlds, like a villain who can use both dark magic and the power of the Titans. It makes for some exciting plotlines as they have to learn to work together.
One common theme is identity. Since Percy is reincarnated in a different setting, he often has to figure out who he is in this new life. Another theme is adaptation. He has to adapt to new rules, powers, and cultures in the crossover world. For example, if he's reincarnated into a world with different magic systems, he has to learn how to use them.
I really like 'Percy in the Marvel Universe'. In this fanfiction, Percy gets transported to the Marvel universe. He has to figure out how to get back home while also dealing with all the superheroes and villains there. It shows his character development as he tries to adapt to this new and very different world. The story also has some interesting pair - ups, like Percy and Spider - Man becoming friends and having adventures together.
One great Percy Jackson and Immortal crossover fanfiction is 'The Immortal Demigod'. In this story, Percy discovers he has an immortal side due to some ancient magic. It's full of action and interesting character interactions. The author does a great job of blending the two worlds together.