Nico di Angelo could be a really interesting character in this kind of fanfiction. He could be the mysterious new student who has his own secrets and past traumas. He might befriend Percy at first, which makes Annabeth a bit suspicious. As the story progresses, Nico's backstory could be intertwined with the drama between Percy and Annabeth, like he has some connection to a mystery at the school that affects their relationship.
Grover could be a great addition. He could be the goofy but loyal friend who always gets caught in the middle of Percy and Annabeth's drama. For example, he might accidentally spill some secrets that cause more trouble between them. Another good character could be Clarisse. She could be the school bully who has a grudging respect for Percy and Annabeth but still tries to cause problems for them now and then.
I think Thalia would be an excellent character to include. She could be the cool, older sister - like figure to Percy. Maybe she transferred to their high school and now has to deal with the drama that Percy and Annabeth are in. She could also give Annabeth some advice about her relationship with Percy. Also, Tyson could be included as Percy's half - brother who is a bit of an outcast at school and Percy and Annabeth have to protect him from the bullies, which adds another layer of drama.