A really interesting plot would be if there was a prophecy related to the Argo. For example, it might be foretold that the Argo must travel to a certain forbidden place to retrieve an ancient artifact that could either save or destroy the demigod world. And the crew has to decide whether to trust the prophecy and embark on this dangerous journey. There could also be a plot where some of the crew members start having strange dreams that seem to be leading them to a hidden mystery related to the Argo's origin.
It contributes by providing more in - depth exploration of Percabeth's relationship. Fans get to see different aspects of their love and how it develops during the Argo 2 adventures. It also adds new storylines to the existing Percy Jackson universe, keeping the fandom engaged.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). There are tons of 'Percy Jackson Argo' fanfics there. Just use the search function and type in relevant keywords. Another place could be FanFiction.net, which also has a large collection of fan - created stories.
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.
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.
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.