Perhaps Percy is sent to the mental hospital because his demigod abilities are misdiagnosed as schizophrenia. In the hospital, he befriends a girl who seems to have some strange powers of her own. Together, they discover that the hospital is being used as a cover for a monster lair, and they must fight to escape and warn the other demigods. The mental hospital setting adds an interesting layer of secrecy and confinement to the story.
One idea could be Percy starts having visions related to his demigod adventures in the mental hospital. The staff think it's part of his mental illness, but it's actually his connection to the Greek world trying to reach him. Maybe he meets other patients who are actually demigods in hiding too, and they have to figure out how to use their powers subtly without getting caught.
One idea could be that Percy starts seeing strange things in the mental hospital that are actually manifestations of Greek monsters from his past. Maybe he has to convince the doctors and other patients that he's not crazy while secretly fighting off these threats.
Another possibility is that Percy has suffered some sort of mental trauma from his battles. He's having nightmares and flashbacks, and his friends think the mental hospital can help him. But once inside, he realizes that there are dark forces at work in the hospital. He has to use his demigod powers subtly to protect himself and the other patients from these unseen threats.
One possible plot could be that Percy wakes up in the mental hospital with no memory of how he got there. He starts to notice strange things like the nurses and doctors seem to have an otherworldly aura. As he tries to regain his memory, he discovers that the hospital is a front for some sort of mythological experiment. He then teams up with other demigods who are also trapped there to escape and expose the truth.
One idea could be that Percy encounters a sea monster with tentacles in a new, uncharted part of the ocean. The tentacles could be enchanted and try to trap him, but he uses his water powers to escape. Another plot could involve a tentacle - like creature that is actually a guardian of an ancient underwater temple that Percy needs to enter. Maybe the tentacles are made of some kind of magical energy that he has to figure out how to get through.
One idea could be that Percy has to seek Hephaestus' help to repair a powerful weapon that is key to defeating a new threat. Maybe the weapon was broken in a battle against a mysterious monster. Another plot could involve Hephaestus tasking Percy with retrieving a special metal from a dangerous location, like the heart of an active volcano, in order to create a new, even more powerful weapon for the demigods. And perhaps there's a sub - plot where Hephaestus' children are in some sort of trouble and Percy has to team up with them to solve the problem.
One idea could be Percy having a vision or encounter with Hestia that leads him to a hidden part of the Underworld where the warmth of Hestia's hearth is the only thing keeping a powerful and dangerous entity at bay. He has to work with Hestia to keep it that way.
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.
It's possible that the main antagonist is a new mythological creature that has the ability to manipulate minds. It has lured Percy and other demigods to the mental hospital and is slowly driving them insane in order to feed off their fear and chaos energy.
Well, he might meet other characters who also claim to have had strange experiences. They could form a sort of alliance, thinking they are all in the same boat, not realizing Percy's experiences are real in the context of the Percy Jackson universe. They could plan an escape together, believing they are being wrongly held.
Another plot could involve Percy's friends getting accidentally transported to a different realm in the Percy Jackson universe. They have to rely on their friendship and the skills they've learned from Percy to survive and find their way back. For example, they might end up in the Underworld and have to navigate past various challenges without Percy at first.