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.
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.
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.
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.
One potential new character could be a scientist, Dr. Thompson, who is studying the strange phenomena in Alaska that are actually related to the magical world Percy is part of. He initially doesn't believe in the magic but as he witnesses Percy's powers, he becomes an ally. There could also be a group of Inuit shamans who have their own powers and traditions. They might initially be wary of Percy but then come to respect him and work together with him to solve a problem that is endangering both the magical and non - magical parts of Alaska.
There could be a strict Roman professor who is very traditional and gives Percy and Annabeth a hard time in their classes. This professor might not trust the Greek demigods at first and constantly tests them. Another potential character could be a Roman demigod who becomes their friend. This demigod could introduce them to all the cool spots in New Rome and help them understand the Roman way of life better.
There could be a new bully at Goode who targets Percy because he senses Percy is different. This bully might turn out to have some connection to the mythological world, like being a descendant of a minor god.
A new teacher who is actually a disguised satyr could be introduced. The satyr could be there to keep an eye on Percy and make sure he doesn't accidentally expose the world of demigods. He could be a bit of a comical character, always getting into trouble with the school rules while trying to protect Percy.
There could be a strict drill sergeant as one of the main characters. This person would be constantly pushing Percy to his limits and teaching him discipline. Another character might be a fellow student who becomes Percy's best friend. They could support each other through the tough times at military school.
There could be a really strict but fair headmaster who has a unique way of teaching magic. He might be an old wizard with a lot of secrets.
There's a chance that Percy meets the personification of Tartarus itself. It could be a shadowy, all - powerful being that tries to break Percy's spirit. Percy, being the brave hero he is, would have to resist and find a way to either outwit or overpower this entity in order to continue his journey in Tartarus.