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.
One idea could be that the demigods from Percy Jackson's world have to team up with the vampires from Twilight to fight a common enemy, like an ancient and powerful dark force. Maybe a primordial being in the Percy Jackson universe has awakened and its influence is spreading, causing chaos even in the Twilight world, so they must combine their powers.
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.
Maybe there could be a new threat that can only be defeated by combining the magic of the Greek demigods and the Egyptian magicians. For example, a powerful monster that is immune to the weapons of one group but vulnerable to the powers of the other. Percy and his friends would have to team up with Carter, Sadie and their crew to take it down. They would need to learn about each other's worlds and powers along the way, which could lead to some interesting character interactions.
One idea could be that the wizarding world discovers the existence of demigods. Harry and his friends team up with Percy and his crew to fight a common enemy that threatens both their worlds, like an ancient, powerful dark force that feeds on magic and the power of the gods. For example, a new kind of dark wizard who has made a pact with a minor, evil god.
One plot idea could be that Percy Jackson discovers a magical artifact that somehow links his world to the Marvel Universe. Thor senses the power of this artifact and comes to investigate, leading to a meeting with Percy. Meanwhile, the Avengers also get wind of it and think it could be a threat. So, they all end up in a big showdown where they have to figure out if they're on the same side or not.
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.
One possible plot could be that the Volturi from Twilight discover the existence of demigods from the Percy Jackson world. They see the demigods as a threat to their vampire supremacy. Percy and his friends have to team up with some of the more friendly vampires, like the Cullens, to fend off the Volturi. This would bring together the magic and powers of both universes in an epic battle.
In a fanfic, perhaps Percy and his friends accidentally stumble upon Medusa's lair while on a quest. But instead of immediately attacking, Medusa offers them a deal. She says she will give them a valuable clue to complete their quest if they help her get revenge on one of the minor gods who wronged her in the past. Percy and his friends then have to decide whether to trust Medusa or not.
One idea could be that the demigods from Percy Jackson's world accidentally end up in the Descendants' universe. They could team up with the VKs (Villain Kids) to face a common threat that is related to both Greek mythology and the magic in the Descendants world. For example, an ancient Greek monster that has been awakened by the dark magic in the Isle of the Lost.
Another interesting plot could involve a prophecy that links the Dragonborn and Percy. They both have destinies to fulfill, and their paths cross when they realize that they need to combine their powers. For example, the Dragonborn's combat skills and the ability to absorb dragon souls, along with Percy's control over water and his demigod powers, could be used to defeat a dark force that threatens both their worlds. It could also explore how the different magic systems interact, like the magic of Skyrim and the magic in the Percy Jackson universe.