One idea could be that the new girl is a demigod from a very rare and powerful lineage. For example, she could be a descendant of a primordial god that no one has seen in centuries. This would bring a whole new dynamic to Camp Half - Blood as everyone tries to figure out her powers and where she fits in.
She could be the daughter of a minor god that hasn't been introduced much in the original Percy Jackson series. For instance, the daughter of Hecate. This would give her powers related to magic, which would be really cool in the context of the story. She could use her magic to help Percy and his friends in battles or to solve some of the mysteries they encounter.
A plot could be that Percy is sent on a quest that leads him to the 'New Girl' universe. He has to find a magical item hidden in the loft. The 'New Girl' characters think he's crazy at first, but as they see the magic unfold, they help him. Another plot could be that one of the 'New Girl' characters discovers they are a demigod. Jess, for instance, realizes she has demigod powers and Percy has to train her. This would bring a whole new dynamic to the loft as she tries to balance her normal life and her new demigod life.
She could be really shy at first. Maybe she comes from a place where she was always bullied for being different, so when she arrives at Camp Half - Blood, she has a hard time opening up to others. But as she discovers her powers and makes friends, she slowly becomes more confident.
One interesting crossover could be Percy Jackson finding himself in the world of 'New Girl'. He might use his demigod skills to solve the zany roommate problems. For example, when Nick and Schmidt have one of their epic arguments, Percy could use his water powers to cool them down, literally. Maybe he'd also introduce the 'New Girl' characters to some of his demigod friends like Annabeth, and they'd all go on adventures in Los Angeles together.
One interesting crossover could be a scenario where Jess from New Girl somehow stumbles into the world of Percy Jackson. Maybe she thinks it's all part of some elaborate prank at first. For example, she could meet Percy and mistake his sword for a prop. Percy would be confused by her modern and rather eccentric behavior. Another idea could be that the loft in New Girl becomes a haven for demigods on the run. They use it as a hiding place and Jess and the gang have to deal with all the chaos that comes with having demigods around, like strange monsters showing up or magical items causing havoc in the loft.
Well, the new girl could be a demigod who doesn't know her true identity at first. She might arrive at Camp Half - Blood and start to show extraordinary powers. Maybe she has a special connection to Percy Jackson, like they share a common enemy that they have to face together. This could lead to an exciting adventure filled with battles against mythical creatures and the discovery of her own past.
First, you need to know both universes well. For 'New Girl', understand the characters' personalities like Jess's quirkiness, Nick's laid - back nature, etc. For 'Percy Jackson', know about the demigods, the gods, and the world of Camp Half - Blood. Then, think of a unique plot. Maybe the New Girl characters discover they are demigods. Or the Percy Jackson characters visit the loft in 'New Girl'.
Another fanfic that's worth checking out is 'Percy Jackson's New Girlfriend from New Girl'. This fanfic focuses on a romantic relationship between a Percy Jackson character and a character from New Girl. It's a bit of a different take as it explores the dynamics of a relationship between two very different fictional worlds. The author manages to make it seem believable and engaging.