Maybe in the fanfiction, if someone on the Argo 2 endangered his friends, Percy would get angry. He's very protective of his friends, like Annabeth. If any harm came their way because of someone's recklessness on the ship, that could set him off.
They might face new and strange monsters. For example, they could encounter a sea - serpent that has the power to control the weather around the Argo 2. Percy would use his water - controlling abilities to try and fend it off while Annabeth comes up with a strategic plan to defeat it.
When Frank gets hurt on the Argo 2 in fanfiction, it could set off a chain of events. His injury might make the group more cautious, or it could even lead to some internal conflicts. For instance, some might blame others for not protecting Frank well enough. Meanwhile, Frank himself might have to struggle with his physical pain as well as any psychological impact of the injury, like fear of not being able to contribute to the group's mission as much as before.
Jason is likely to be another main character. Since he has his own set of skills and knowledge, he might have an interesting relationship with Percy in this story. Maybe he's a bit jealous at first of Percy's control over the ship, but then they end up working together really well. And of course, Piper could be there too. She might use her charm - speak abilities to help the crew communicate with any strange creatures they encounter during Percy's time controlling the Argo 2.
It could be an enemy that manages to sneak onto the Argo 2. Maybe a monster that they thought they had defeated before but actually just bided its time and then attacked Percy when he was least expecting it.
Well, he might be unable to perform his duties on the ship for a while. His friends would surely be worried sick and would probably do everything they could to nurse him back to health. Maybe Annabeth would take charge of his care, using her wisdom to find the best way to heal him.
He might start yelling. Percy is known for his passionate nature, so when angry on the Argo 2, he could raise his voice at those who he thinks are at fault.
The main characters are clearly Percy and Annabeth. Percy, the son of Poseidon, is known for his courage and his ability to control water. Annabeth, the daughter of Athena, is highly intelligent and strategic.
Well, it could be about Percy and Annabeth having some sweet, romantic moments on the Argo 2. Maybe they're sharing secrets, or just enjoying the journey together while facing some minor challenges on the ship.