Another theme is adaptation. Percy has to adapt to the very different world of Frozen, with its different rules, culture, and climate. This often involves him learning about the politics of Arendelle and how to interact with its people while still being true to his own nature.
A powerful ice giant could be the antagonist. This ice giant could have a grudge against Percy for some past encounter and uses its ice - magic to freeze him. It wants to keep Percy out of the way while it tries to invade Camp Half - Blood or other places important to the demigods.
One great Percy Frozen fanfiction is 'Percy in Arendelle' where Percy somehow gets transported to the world of Frozen. It has an interesting plot as Percy tries to adapt to the cold climate and the new magic system while also befriending Elsa and Anna. The author does a great job of mixing the two universes.
In a Percy Jackson - Frozen fanfiction, perhaps Annabeth could meet Anna. Annabeth would be impressed by Anna's determination and loyalty. They could go on an adventure in the Arendelle kingdom, with Annabeth using her strategic mind to solve problems that the Frozen world is facing, like a strange curse that is making the ice in the kingdom melt uncontrollably.
Well, Percy's ability to control water and Frozen characters' ice powers could create some cool interactions. For example, Percy could make a stream of water and Elsa could freeze it to create an ice bridge. It would be a great way for them to traverse difficult terrains.
One idea could be that Percy is frozen in ice due to a powerful curse from an ancient enemy. His friends in Camp Half - Blood have to go on a quest to find a magical item that can break the curse. Maybe it's a rare flower that only blooms in a certain realm.
One interesting plot twist could be that Percy's water powers somehow interact with Elsa's ice powers in unexpected ways. Maybe when they meet, their powers combine to create a new form of frozen water element that has unique properties. Another could be that the demigods from Percy Jackson's world have to deal with the magical cold of Arendelle, which is a whole new kind of challenge compared to their usual Greek - related threats.
I think a really intriguing pairing would be Grover and Olaf. Grover is this nature - loving satyr, and Olaf is this innocent and fun - loving snowman. Grover could be constantly worried about Olaf melting in the wrong conditions, while Olaf could introduce Grover to the joys of just having fun without so much worry. Also, Jack Frost from the Frozen - adjacent lore and Percy could be a great pair. They both have a connection to the cold and water in different ways, and their powers could either clash or work together in interesting ways.
Some interesting Frozen 2 fanfiction plot ideas could revolve around the idea of a magical item. For example, there could be a magical crystal hidden deep in the forest that has the power to either save or destroy both the forest and Arendelle. Elsa and her friends embark on a quest to find this crystal before it falls into the wrong hands. Another idea is that a dark force from outside the known world tries to invade the forest and Arendelle, and the characters have to unite not only the people of Arendelle and the forest but also other magical beings to fight against it. Also, a plot could be centered around a prophecy that was never fully revealed in the movie, and Elsa and Anna must figure out what it means for their future.