One interesting plot could be Percy using his water powers in Asgard. Since Asgard has its own unique environment, his powers might interact in unexpected ways with the magical elements there. For example, he could create ice sculptures in the middle of a battle, which not only serve as a defense but also as a distraction to the enemies.
His physical strength might increase. Thor is known for his great strength, and as his adopted son, Percy could inherit some of that. He might be able to lift heavier objects or fight more powerfully in close - combat situations. Maybe he could even hold Mjolnir for a short period of time, which would be a huge boost to his powers and status in both the Greek and Asgardian worlds.
The Son of Thor would interact in diverse ways. With Annabeth, he could have some intellectual exchanges. She might be intrigued by the Norse mythology he represents and how it compares to Greek mythology. Grover would be friendly towards him, and they could share stories about their different worlds while on a journey. As for Percy's other friends, the Son of Thor would bring his own sense of honor and strength, which could earn him respect or cause some friction depending on the situation.
In this fanfiction, there might be a lot of focus on Percy's relationship with the other wolves in Lupa's pack. He could learn their ways of survival, their hierarchy, and how to be a part of their community. This would be a great way to explore his adaptability and growth.
The setting of the story might shift a bit. Instead of always being at Camp Half - Blood or on quests related to the Greek gods, Percy could be in the territory of the wolves. There could be new threats and challenges there, like rival wolf packs or ancient enemies of Lupa. And all these elements would make for an exciting and different take on the Percy Jackson universe.
In most Percy Jackson canon, there is no relation to Thor. However, in fanfiction, anything can be possible. It could be that the author has created a unique crossover where Percy Jackson has some connection to being the heir of Thor, perhaps through some magical or divine intervention that the fanfic writer has dreamed up.
Well, it could be about Percy having to deal with the powers and heritage that come with being the adopted son of Pontus. Maybe he discovers new underwater abilities that are different from his Poseidon - given powers. He might also have to face enemies who are after the secrets Pontus has.
One possible plot could be Percy's struggle with his new identity as the adopted son of Zeus. He might face envy from other demigods who don't understand why he was chosen. He could also have to deal with Zeus' overbearing nature as he tries to train Percy in godly powers. And there would likely be new quests that involve both his ties to Poseidon and his new relation to Zeus.
Well, it could be about Percy having to adapt to his new divine family. Maybe he has to learn special water - related powers from Amphitrite that are different from what he already knows. He could also face challenges from other sea deities who are jealous of his new status.
Perhaps the story could be about Percy facing discrimination from other demigods due to his new relation to Pluto. He is then forced to prove himself not only as a hero but also as a worthy adopted son of Pluto. He trains hard to master the powers and knowledge that come with his new status. He also tries to find a way to use his underworld - related abilities for the good of all demigods, like using his connection to the dead to get information about future threats to the demigod world.