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.
Well, it could start with a magical accident. In the Percy Jackson universe, a spell gone wrong sends Percy, Annabeth, and Grover into the land of Alagaësia from Eragon. There, they discover that the demigod powers Percy has are seen as a strange and new form of magic. Eragon is initially suspicious of them but realizes they can help in his fight against Galbatorix. They combine their skills, Percy's water - controlling powers and sword - fighting skills, along with Annabeth's strategic mind and Grover's nature - sensing abilities, with Eragon's dragon - riding and magic - wielding skills to take on the dark forces.
One idea could be that Percy and his friends are on a quest and accidentally stumble into Alagaesia, the world of Eragon. There, they meet Eragon and Saphira. The demigods' powers might be seen as strange magic by the people of Alagaesia. Percy could use his water - controlling abilities to help Eragon in a battle against some new threat that is both a danger to the demigods' world and Alagaesia, like a powerful water - based demon. They would have to learn to work together, with Percy teaching Eragon about the modern world's concepts and Eragon showing Percy the ways of magic in his world.
The plot could involve a villain who has found a way to cross between the two worlds. This villain starts causing chaos in both the world of Percy Jackson, like turning demigods against each other, and in Eragon's world, by disrupting the dragon - rider bond. Percy and Eragon, being the main heroes, have to team up. They start by trying to understand each other's powers and the rules of their respective worlds. Along the way, they make new friends and allies from both worlds and face many challenges together until they finally defeat the villain and restore peace in both their worlds.
Definitely Percy and Eragon. Percy with his quick - witted and brave nature would have an interesting dynamic with Eragon, who is more solemn and duty - bound. They could learn a lot from each other, like Percy teaching Eragon about having a sense of humor even in tough situations, and Eragon showing Percy the importance of loyalty to a cause.
Annabeth Chase could be an interesting character to focus on. She is highly intelligent and strategic. In a crossover, she could use her knowledge of architecture and battle strategies to help Eragon and his allies. She might study the magic in Alagaesia and find similarities or differences with the powers of the demigods. Her relationship with Percy could also be explored in a new light, especially when they are in a completely different world. How would they support each other in this new and strange environment? And how would she interact with the characters in Eragon's world?
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 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.