A third idea is for a prophecy to bring them together. The prophecy could foretell of a hero from each world coming together to stop an ancient evil that is trying to break through the barriers between their universes. They would have to overcome cultural differences and learn to trust each other quickly in order to face this great danger.
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.
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.
Another idea is that Peter discovers the existence of demigods while investigating a series of strange disappearances in Central Park. He stumbles upon Percy who is on a quest. They initially have some misunderstandings as they come from such different worlds, but then they figure out that they can help each other. Percy helps Peter understand the magical side of things, and Peter helps Percy with his knowledge of the city's layout and technology.
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.
Another possibility is a story where the gods from Percy Jackson's world interact with the gods in the God of War universe. The gods in Percy Jackson are more involved in the lives of their demigod children, while the gods in God of War are often more distant and feared. This could lead to some interesting power struggles and misunderstandings. For example, Zeus in Percy Jackson might have a very different relationship with his children compared to Zeus in God of War.
Another idea is a setting where the two worlds are merging. Percy and Magnus find themselves in a strange new place that has elements of both Camp Half - Blood and the Hotel Valhalla. They have to figure out how to survive in this new world while also dealing with the chaos that the merging is causing. The characters from both series could interact in interesting ways, like Annabeth and Samirah comparing their knowledge of architecture and magic respectively.
Another possibility is a crossover of the settings. The Camp Half - Blood could be merged with an area from the Avatar world, like the Air Temple. Demigods and benders would have to learn to co - exist and use their powers together. Maybe Percy could learn water - bending techniques from the water benders to enhance his control over water, which is already one of his powers. And the Avatar could learn about the Greek gods and use that knowledge to gain an edge in his battles.
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.
A crossover could also involve a prophecy that links the two worlds. For example, a prophecy states that only the combined powers of a wizard from Hogwarts and a demigod from Camp Half - Blood can defeat an ancient evil that is rising again. Harry and Percy are the ones chosen, and they have to learn about each other's strengths and weaknesses in order to fulfill the prophecy. They could travel between the two worlds, recruiting allies from both sides.
A good crossover idea is that there's a spell gone wrong in the wizarding world that starts to affect the boundaries between the mortal world and the world of the Greek gods. Hermione, being the brilliant witch she is, tries to figure out a solution, and Percy, with his knowledge of the Greek world, gets involved. They could travel through different dimensions together, facing challenges from both magical creatures and mythical beasts.