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.
One new character could be a girl who is majoring in archaeology. She has a fascination with Greek artifacts and unknowingly stumbles upon a powerful cursed item on campus. Percy has to help her deal with the consequences. There could also be a group of students who form a sort of 'mythology club' on campus. They initially think Percy is just another enthusiast, but as things get dangerous, they learn the truth and become his friends and helpers. And perhaps a centaur who disguises himself as a visiting lecturer and gives Percy some valuable advice on how to handle college and his demigod life at the same time.
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.
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 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.
He could meet some Aboriginal heroes or spirits. They might have their own powers and knowledge that Percy can learn from.
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.
There could be a demigod who is the child of a minor god that we haven't seen much in the original series. For example, the child of Hebe, the goddess of youth. This character could bring a fresh perspective with their powers related to rejuvenation and vitality.
Some of the more traditional and rule - following demigod groups at Camp Half - Blood could be against him. They believe in following the established ways and Percy's rogue behavior goes against that. They might see him as a troublemaker and try to bring him back to the 'right' path.
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.
A new character could be a transfer student from another demigod camp. This student has a different set of powers and a unique backstory related to a less - known Greek god. They could initially clash with Percy but then become great friends as they face challenges together.
There could be a new camper who has some really unique powers. Maybe a child of a minor god that we haven't heard much about in the original series. This new character could be both a friend and a rival to Percy.