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.
Another theme is identity. Percy already has a complex identity as a demigod, but when crossed over with immortals, he has to re - evaluate who he is. He might question if he could become an immortal or if he should stay true to his demigod roots. This is seen in a lot of fanfictions where Percy is faced with choices that could change his very nature.
Well, the plot could involve Naruto's ninja skills being pitted against Percy's demigod powers. Maybe they meet in a dimension where both their worlds collide. Naruto could use his shadow clones to outnumber Percy's foes, while Percy could use his control over water to counter Naruto's fire - style jutsus.
Well, one idea for this crossover could be that Savitar somehow ends up in the world of Percy Jackson. Maybe he's chasing after some new kind of speed - the speed of a demigod? And Percy has to figure out how to deal with this strange, super - fast being who doesn't seem to follow the normal rules of the Greek myth world.
Naruto would probably be very curious about Percy's powers. He'd be excited to see someone who can control water in such a unique way. Percy, on the other hand, might be a bit wary of Naruto at first, but would soon be impressed by his ninja skills. They'd likely start by testing each other's abilities in a friendly spar.
Another idea is that Sophie Foster from KotLC travels to the Percy Jackson universe. She could be mistaken for a demigod at first. She would have to learn about the Greek gods and monsters. Her telepathic abilities would be really useful in the Percy Jackson world. For example, she could communicate with some of the monsters to find out their plans. And Percy and his friends would help her understand this new and dangerous world.
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 This could cause him to be more withdrawn at first.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.
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.
One idea could be that Naruto, with his powerful chakra and skills, is somehow transported to the world of Percy Jackson. He might be mistaken for a demigod because of his extraordinary abilities. Naruto could then team up with Percy to fight against a common enemy, like an ancient monster that threatens both their worlds.
Another one to check out is 'Justice League meets Camp Half - Blood'. In this fanfic, the Justice League discovers Camp Half - Blood. It's cool to see how Batman would interact with Chiron, or how Wonder Woman would view the demigod powers. There are a lot of great character moments as the two very different universes collide.