One idea could be to have Percy Jackson transported to the world of Game of Thrones. Maybe he arrives in Westeros and is mistaken for a powerful sorcerer because of his demigod powers. He could get involved in the power struggles between the different houses, using his skills in combat and his ability to control water to his advantage.
Perhaps there could be a crossover of magic. The magic in Game of Thrones is quite different from the powers in Percy Jackson. So, what if the White Walkers' ice magic somehow interacted with Percy's water - based powers? Maybe Percy has to figure out a way to use his powers to stop the White Walkers' advance, while also dealing with the political intrigue of Westeros.
Perhaps there's a plot where the dinosaurs are being used by an evil force. The evil force has found a way to control the dinosaurs and is using them to attack the demigod camps. Percy and his friends then have to figure out how to break the control and save the day. They might find out that the dinosaurs have a connection to an old Greek god or goddess that they didn't know about before.
One idea could be that Percy Jackson discovers a hidden Cybertronian relic. This relic has the power to control water in a way that even Poseidon's trident can't. The Autobots and Decepticons are both after it. Percy has to team up with the Autobots to keep it out of the Decepticons' hands and also figure out how it relates to his world of Greek gods.
In a fanfiction, perhaps the gods in the Percy Jackson universe are aware of Cthulhu as an ancient and powerful being from another realm. They send Percy on a quest to learn more about Cthulhu's weaknesses in case he ever wakes up fully. Percy teams up with some of his demigod friends and they encounter all sorts of Lovecraftian horrors along the way. They soon realize that Cthulhu's power is far greater than anything they've ever faced and they have to rely on their wits and some newfound magic to survive.
In this fanfiction, the gods in Percy Jackson's world are intrigued by Poison Ivy's power. They bring her to Olympus to study her. Percy is assigned to be her guide while she's there. Along the way, they discover that there are similarities between the magic in Poison Ivy's world and the divine powers in Percy's world. They start to experiment with combining their powers, like Percy using his water powers to help Poison Ivy's plants grow in unexpected ways, and Poison Ivy using her plants to create shields for Percy during his training sessions.
One idea could be to have Percy Jackson end up in Middle - earth. He could use his water - related powers to help in battles against Sauron's forces, like using water to put out dragon fire. His demigod skills would be a new element in the LOTR universe.
One idea could be a crossover where the demigods from Percy Jackson's world meet the Grimm sisters. Maybe they team up to fight a common enemy that threatens both their realms, like an ancient evil that has the power to disrupt the balance between the magical world of the Grimm sisters and the mythological world of Percy Jackson.
One idea could be a story where Ichigo, in his godlike form, somehow gets transported to the world of Percy Jackson. He could team up with Percy to fight a common enemy that threatens both their realms. Maybe a powerful ancient being that has the ability to disrupt the balance of souls (from Ichigo's world) and the Olympian order (from Percy's world).
Maybe in the fanfiction, the Gods decide to test Naruto and Percy Jackson by pitting them against each other in a series of trials. This could explore how their different backgrounds and abilities influence their performance in the trials.
Another possibility is a story where Percy Jackson finds himself in the Naruto universe and is taken in by Hestia, who has somehow also made her way there. Hestia could act as a guide or protector for Percy while he tries to figure out how to get back to his own world. Along the way, he meets Naruto and they learn from each other's skills and cultures.
Perhaps a fanfiction where Naruto has a descendant in the future who ends up in Percy Jackson's world. This descendant has some of Kaguya's powers that were passed down through the generations. The story could revolve around how this new character tries to hide their powers at first but then has to use them to fight against the Titans or other threats in Percy Jackson's world, all while trying to find a way back to their own world.