The plot could center around Percy's struggle to fit in at college while still being a hero. He may find that the other students don't understand his need to disappear suddenly when there's a monster attack. He could also get involved in some sort of college - wide mystery that has roots in the ancient world. Like, strange symbols start appearing all over campus that only he can decipher because of his knowledge of Greek and Roman mythology. And he has to team up with some unlikely allies, like a nerdy professor who turns out to have a hidden knowledge of the demigod world, to solve the mystery and save the college from an impending doom.
There could be a new demigod who transfers to Percy's college. This demigod could have powers related to nature, like being able to make plants grow instantly. They would become Percy's ally in dealing with the campus - based mythological threats. Another new character could be a strict dean who is always on Percy's case, not realizing that Percy is actually protecting the college from real danger. And there might also be a mysterious janitor who actually has a deep connection to the underworld and gives Percy cryptic warnings from time to time.
Percy going to Ilvermorny would be a wild ride. First, he'd be amazed by the castle itself. The four houses would be a new concept for him. He might be sorted into a house based on his heroic nature, like Thunderbird perhaps. He'd introduce the idea of Greek gods to the students there, which would cause quite a stir. And his relationship with Annabeth would be put to the test as they are separated by different magical institutions.
He might meet some talented witches and wizards. Maybe there would be a student who is an expert in magical beasts and they could share stories about their encounters with strange creatures.
Percy might meet an old enemy who has somehow been resurrected or changed in the future. This enemy could be more powerful and have a new plan to take over the world or destroy the demigods. Or he could meet a group of time - traveling demigods from an even further future who are trying to fix something in Percy's future that has gone wrong.
Maybe Percy will face new challenges in college like dealing with difficult classes. He could also meet new friends or enemies. And perhaps he'll discover new powers or secrets related to his special nature.
Percy might run into Loki. Loki is known for his trickery. He could either befriend Percy for his own devious plans or try to deceive him. Percy, being used to dealing with tricky situations in his own world, would have to be on his guard against Loki's schemes.
There could be a really smart professor who suspects there's something different about Percy. Maybe a roommate who is into all kinds of strange and supernatural things without actually knowing the truth about Percy.
Percy Jackson himself is of course very popular. His friends like Annabeth Chase also often appear. Grover could be there too, still being Percy's loyal friend. New characters might include college professors who turn out to have some connection to the world of mythology, like a history professor who is secretly a descendant of a minor god.