Another plot could involve Percy being ostracized by some of his friends at Camp Half - Blood because of his connection to Lycaon. But he then uses this as motivation to become stronger. He could go on a solo quest to find a way to redeem the name of Lycaon in the eyes of the gods, which in turn would make his friends see him in a new light.
One idea could be Percy having to face challenges specific to being the 'son of Lycaon'. For example, he might struggle with the werewolf - like instincts that come with that heritage. He could have to prove himself to the other demigods who are skeptical of his newfound origin.
One idea could be Percy having to use his charm powers (from being Aphrodite's son) to charm a powerful, ancient monster into sparing a group of demigods. He might struggle with the morality of using such powers in this way.
One idea could be Percy using Wolverine's healing factor during a particularly tough battle in the world of Greek mythology. Maybe he gets injured by a powerful monster and the unexpected emergence of the healing ability saves him and surprises his friends.
One idea could be Percy having to go on a quest with the children of Dionysus. They could face a new type of monster that is immune to normal weapons but can be defeated by the power of wine, which the children of Dionysus can control. Another could be Percy getting into a friendly rivalry with a son of Dionysus over who can throw the best party at Camp Half - Blood. Maybe they compete to see who can get more demigods to attend their party, and in the process, they learn more about each other's powers.
Perhaps Percy finds out that being the son of Selene gives him a connection to the dreams of mortals. He starts to have strange visions through their dreams and realizes that there is a hidden threat that is using the dreams to manipulate people. He has to figure out how to stop this threat without causing harm to the mortals. He might team up with some other demigods who have powers related to the mind or dreams to solve this mystery.
One idea could be Percy having to face a new and powerful enemy that is specifically targeting the Roman demigods. He could team up with some of his old friends from the Greek side and form an alliance with the Romans to defeat this threat.
One idea could be Percy discovering new powers given to him directly by the creator. For example, he might gain the ability to manipulate time on a small scale, which could add a whole new layer of challenges and adventures as he tries to control this power without causing chaos.
Another plot could involve Percy having to deal with a powerful sea monster that is not from Greek mythology but from some other ancient culture's sea lore. He has to use his skills and the help of his friends in a new and different way to defeat it.
One idea could be Percy exploring his new powers as the 'Son of Darkness'. He might discover abilities that are the opposite of his normal powers, like creating shadows instead of controlling water. Another could be his struggle to fit in with his friends and the demigod community when they view him as different now. He could also face new enemies who are attracted to his new dark nature.
One plot idea could be Percy having to prove himself to the Norse gods. Since he's the son of Odin in this fanfiction, the other Norse deities might be skeptical. He'd have to go on a quest to show his worth, like retrieving a powerful Norse artifact.
One idea could be Percy forming an unexpected alliance with a minor Roman god. In the fanfiction, this god could have a unique power that helps Percy in his quests. For example, a god of illusions who can create decoys to mislead Percy's enemies.