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).
In a fanfiction, Godlike Ichigo might be mistaken for a new demigod in Percy Jackson's world. This could lead to all sorts of misadventures as the characters from Percy's world try to figure out his powers. Meanwhile, Ichigo is just as confused and is trying to find a way back to his own world. Along the way, they could discover that their powers are more related than they thought, perhaps having a common origin in some long - forgotten mythology.
One idea could be that Percy finds himself magically transported to Skyrim. He could use his water - based powers in the frozen landscapes, like creating ice bridges over rivers or using water currents to his advantage in battles against the various creatures in Skyrim.
A possible fanfiction could involve a crossover where some of the Avengers are sent to Camp Half - Blood. Imagine Tony Stark trying to figure out how the magic at the camp works while also being highly amused by the whole concept of demigods. Steve Rogers could bond with some of the more heroic demigods over their shared sense of duty. Meanwhile, Percy and his friends have to keep an eye on the Avengers to make sure they don't accidentally disrupt the delicate balance of the camp. And then, they all have to face a threat that targets both the Avengers and the demigods, like a group of villains who want to steal the powers of both.
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 a fanfic, Percy could be a new student at the academy, but with his demigod powers. His water - controlling abilities would be quite a shock to the vampire and monster students. There could be a plot where some of the vampires want to use Percy's powers for their own gain, leading to an exciting adventure of Percy trying to outwit them.
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 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.
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.