One idea could be that Percy discovers an ancient immortality spell hidden in the depths of Westover Hall. He has to face off against some dark forces that also want the spell for their own evil purposes. Maybe he teams up with some new friends he makes at the hall to keep the spell out of the wrong hands.
Well, in this fanfiction, Percy's immortality could lead to some really interesting character development. He may start to feel lonely as he realizes that he will outlive all of his friends. This could cause him to be more withdrawn at first. But then, as he interacts with the students at Westover Hall, he might find new meaning in his immortality. He could start to see it as a way to protect others not just for a short time, but for as long as he exists. He could also form deep and lasting friendships with those who accept him for who he is, regardless of his immortality.
There might be a fanfiction where an older Percy Jackson goes to Westover Hall undercover to investigate some strange magical occurrences. He teams up with some of the students who have a latent magical ability. In this story, he has to hide his identity while trying to figure out what's going on. The author could play with the idea of Percy using his skills in a more mature and strategic way compared to when he was younger.
One interesting plot could be Percy and his friends having to solve a mystery within Westover Hall that involves an ancient artifact hidden there. Maybe it's a lost weapon of a Greek god that has the power to control the weather. Another plot could be a new character arriving at Westover Hall who is secretly a demigod in disguise, and Percy has to figure out their true identity before a monster attacks. And there could also be a plot where the school is hosting a competition, but it's secretly a test by the gods to see which demigod is the bravest and most worthy.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). They have a large collection of Percy Jackson fanfictions, and you can use the search function to specifically look for ones related to older Percy and Westover Hall. Just type in 'older Percy Jackson Westover Hall' in the search bar.
Percy himself is always an intriguing character to include. His sarcastic humor and his ability to get into trouble and out of it are fun to write about. Annabeth is also great. Her intelligence and her strategic mind can add a lot to the story. Grover is another one. His loyalty and his goat - like tendencies can create some humorous and heartwarming moments. And don't forget about the villains. A well - written villain like a powerful monster or a devious demigod who has a vendetta against Percy can make the story really exciting.
One great Percy Jackson and Immortal crossover fanfiction is 'The Immortal Demigod'. In this story, Percy discovers he has an immortal side due to some ancient magic. It's full of action and interesting character interactions. The author does a great job of blending the two worlds together.
One way it could work is if Naruto's immortality was a result of some powerful magic in the Percy Jackson universe. Maybe he was blessed by a god or came into contact with a magical artifact that made him immortal. His ninja skills would be quite unique in that world and could make for some interesting storylines, like teaching demigods his stealth techniques.
Well, he could potentially use his ninja skills to help the demigods in various quests. Maybe his shadow clone jutsu could be used for scouting or distraction, which would be a huge advantage against the monsters in the Percy Jackson world.
One idea could be Percy exploring different mythologies in his immortal state. Since he has a connection to Greek mythology, he could now travel to other realms related to Norse or Egyptian mythology and interact with their deities. Another could be Percy dealing with the concept of eternal loneliness. He has seen his friends and family age and pass away while he remains immortal.