There could be a fanfic where Percy is kidnapped by a cult that worships an ancient and evil god. They believe Percy has the key to awakening their god fully. They keep him in a secret lair filled with all kinds of magical traps and barriers. Or, perhaps a group of Titans who were thought to be defeated manage to come back and kidnap Percy as he is seen as a major threat to their potential return to power. Another scenario is that a powerful wizard from a different magical realm kidnaps Percy, thinking he can use Percy's unique demigod abilities to enhance his own magic.
Well, a plot could be that Percy is kidnapped by a sorcerer who has a vendetta against Poseidon. The sorcerer thinks that by taking Percy, he can get revenge on the sea god. Another could be that some jealous demigods from another camp, who feel overshadowed by Percy's fame, kidnap him. They might try to make him look bad in front of the other demigods. Also, it could be that a mysterious force from the Underworld kidnaps Percy because they fear his growing power and want to keep him out of the way.
There could also be a plot where the sirens are not the typical villains. In this fanfiction, they could be victims of a greater evil in the ocean. Percy has to team up with them to fight this common foe. It would be a great twist on the traditional view of sirens in the Percy Jackson universe.
One possible plot could be Percy getting a special power from Apollo's blessing. For example, he might gain the ability to heal faster, which would be really useful in his battles. He could use this new power to save his friends in a dangerous situation, like when they are facing a powerful monster and his friends are severely injured.
One possible plot could be Percy being stuck in a time loop where he has to keep saving Artimis from a recurring threat. Maybe a powerful Titan is constantly finding new ways to capture her, and Percy has to figure out the pattern within the loop to stop it for good. Another idea is that the time loop is a result of a curse placed on Artimis, and Percy has to team up with the hunters of Artimis to break the curse before the loop consumes them all.
It could be Luke Castellan. He has a history of being against Percy and the Olympians. He might kidnap Percy to gain an advantage in his own quest for power. He could use Percy as a bargaining chip with the Titans or other powerful forces.
In some fanfictions, Typhon is not just a mindless monster. He might have motives and desires. For instance, he could be seeking revenge against the gods for imprisoning him. This makes him a more complex character and gives the story more depth. Writers can then explore the moral implications of whether the demigods should just destroy him or try to reason with him.
A really interesting plot could be that Sonic is kidnapped into another dimension by a powerful being. In this dimension, the laws of physics are different, and Sonic has to figure out how to use his speed in new ways to escape. His friends back in his own dimension are desperately trying to find a way to bring him back. Meanwhile, Sonic meets some strange new allies in this other dimension who help him in his quest to return home.
Another idea in Percy Jackson and Demeter fanfiction is the idea of a friendship or a mentorship between them. Demeter could be like a mother figure to Percy, guiding him not only in matters related to nature but also in his personal growth. She could give him advice on how to deal with his complex family situation, using examples from the natural world she governs. This would add a very interesting emotional depth to the story.
One possible plot could be that the kidnappers are actually fans who have gone too far in their obsession. They take Tom Holland, thinking they can have him all to themselves. Another could be that he's kidnapped as part of a ransom plot by a criminal group who wants a large sum of money from his management. Maybe it's also a case where a supervillain from one of his movie universes kidnaps him for some strange, other - worldly reason.
One possible plot could be Percy having to deal with new powers. He might struggle to control them at first, like accidentally causing thunderstorms when he's angry. Another plot could involve other characters' reactions. His friends might be in awe or a bit scared. For example, Annabeth could be worried about how this change will affect their relationship. Also, Percy could face new enemies who are jealous of his new god - like status or want to use his powers for their own evil plans.
Perhaps Octavian's sickness is a way for the author to explore themes of forgiveness and acceptance. He could be a really unlikable character at first, but as he gets sick, he starts to change. The other characters see this change and start to question their own prejudices against him. His sickness could be a catalyst for him to make amends with those he has wronged in the past. And the story could end with him either fully recovered and a changed person, or with his death being a turning point for the other characters to become better.