Well, a cool plot might be Percy getting lost in time and ending up in Ancient Greece during the Trojan War. He could then have to figure out how to get back to his own time while also getting involved in the events of the war. Maybe he tries to change the outcome of the war, but realizes that doing so could have disastrous consequences for the future. Or perhaps he discovers that there's a secret reason why he was sent back in time, like to retrieve an important artifact that was lost during the war.
One idea could be Percy having to mediate a major conflict between the Roman and Greek demigods that threatens to spill over into the mortal world. He could use his unique position as son of both cultures to find common ground.
One idea could be that Fem Percy, as a daughter of Poseidon, is underestimated in a male - dominated Athens. She has to prove herself in the various trials and challenges set by the city - state, like competing in a special athletic event where only men are expected to participate. This could lead to her making new allies and enemies alike.
In a fanfic, perhaps Percy and his friends accidentally stumble upon Medusa's lair while on a quest. But instead of immediately attacking, Medusa offers them a deal. She says she will give them a valuable clue to complete their quest if they help her get revenge on one of the minor gods who wronged her in the past. Percy and his friends then have to decide whether to trust Medusa or not.
One interesting adventure could be Percy exploring the lost city of Atlantis in Ancient Greece. He might face sea monsters and ancient traps while trying to uncover the secrets of the city.
One idea could be Percy discovers he has a new ability related to his gills that allows him to communicate with underwater creatures in a more profound way. Maybe he can understand their ancient languages and has to use this new skill to solve an underwater mystery that threatens both the sea world and the surface world.
A great plot for a 'Percy Jackson at School' fanfic would be Percy competing in a school - wide competition that is secretly a test by the gods. The tasks in the competition could be related to the skills he has learned in his demigod adventures, like sword - fighting or outsmarting a maze - like obstacle. Also, he could befriend a mortal student who starts to suspect there is something different about Percy and his friends, and Percy has to decide whether to reveal the truth or keep the mortal in the dark.
Perhaps being reborn as a child of Poseidon but with a twist. Instead of having the typical water - based powers, you have the power to communicate with sea creatures in a way that no one else can, like understanding their emotions and memories. Or being reborn as a demigod who has lost their memory but slowly regains it as they go on quests and face challenges, and each recovered memory reveals a crucial part of their past and a new power or ability.
Well, perhaps the succubus is sent by an enemy of the gods to disrupt Percy's relationships with his friends. She starts causing jealousy and strife among them by using her alluring powers. Or maybe she's tied to an ancient prophecy that Percy is involved in, and he has to either defeat her or convert her to the side of good to fulfill the prophecy.
One idea could be that Percy adopts a young demigod who has a very rare and powerful ability. Percy has to teach this new demigod how to control their powers while also protecting them from monsters who are after the new kid because of their potential. Another could be that the adopted demigod is from a different pantheon entirely, which causes some interesting cultural clashes and misunderstandings within the Camp Half - Blood environment.
One idea could be a story where Percy and Herera have to team up to save a group of demigods who are trapped in an ancient, cursed labyrinth. They face various monsters and puzzles along the way.