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.
They could be brought together by a prophecy. For example, a prophecy states that only the combined power of a powerful wizard and a demigod can stop an ancient evil from awakening. Hermione and Percy are the ones chosen. Along the way, they discover that their two worlds are more connected than they thought, and they have to learn from each other's skills and cultures to succeed.
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.
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.
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.
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.
First, know both universes well. For a 'Percy Jackson Crossover Fanfic', you need to be familiar with the Percy Jackson world, like the gods, demigods, and Camp Half - Blood. Also, understand the other universe you're crossing it with. This knowledge will help you create believable interactions between characters.
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 the demigods from Percy Jackson's world end up in Forks for some reason. Maybe they are on a quest that leads them there. And they cross paths with the vampires and werewolves from Twilight. For example, Percy could use his water powers to fend off some danger that the Twilight characters are facing, like a wildfire started by a vampire's power going out of control. This would create an interesting dynamic as the two different mythologies collide.
A cool plot might involve a character from the Percy Jackson series getting lost in the Kane world. For example, Percy could end up in the Kane world and not understand how their magic works. The Kane siblings would have to help him while also dealing with their own problems, like the threat of some dark magician. At the same time, Percy's friends from his world are trying to find a way to bring him back, leading to an interesting crossover of events and character interactions.