A demigod who has the power to communicate with the dead. Percy adopts this troubled soul who is constantly haunted by the voices of the deceased. Percy has to help them come to terms with their power and find a way to use it for good. This would be an interesting dynamic as Percy is used to dealing with more physical threats, while this demigod's problems are more of a psychological and spiritual nature. They could go on quests to places like the Underworld to better understand the demigod's power and how it relates to the world of the living and the dead.
I think a character with the ability to control time would be really interesting. Imagine Percy having to deal with a demigod who can accidentally mess up the time continuum. It would create all sorts of wacky situations at Camp Half - Blood. Like, one moment they're having breakfast, and the next, it's suddenly midnight because the adopted demigod made a time - related mistake.
A demigod who is a descendant of Hecate but has no idea how to use their magic properly. Percy adopts this demigod, and they have to learn about magic together. Since Percy is more of a sword - and - water - powers kind of guy, it would be a journey of discovery for both of them. This demigod could bring a whole new element of mystery and magic to Percy's life, and they could encounter all kinds of magical creatures and challenges that Percy has never faced before.
One challenge could be dealing with the child's past traumas. If the child has been through a lot, like being orphaned or facing monster attacks on their own, Percy would have to help them heal. He's not a trained psychologist, so it would be difficult for him to know exactly how to handle it.
It could be a child of a minor god who has been overlooked. Maybe the child of Hecate, a young demigod with some really interesting magic powers that Percy and Artemis see potential in.
She could be the daughter of a minor god that has been forgotten or shunned. For example, the daughter of Hecate's lesser - known cousin who has some magic abilities but no real place in the demigod world until Percy takes her in.
Perhaps a half - human, half - nymph character. This new character could have a special connection to nature, being able to communicate with plants and animals in ways that even Percy can't. In the context of a champion - themed fanfiction, they could be a wild card. They might not be fully trusted by the demigods at first because of their nymph heritage, but prove to be an invaluable ally in the end, using their unique abilities to help the champions in their quests.
Annabeth from Percy Jackson could be the most interesting. She's highly intelligent and strategic. In a crossover with Twilight, she would be the one trying to figure out how the vampires work and how to use their abilities to their advantage. She might also be a bit suspicious of them at first and would be constantly analyzing their every move, which could lead to some really engaging scenes in the fanfic.
It could be Carter Kane. His leadership skills and his deep knowledge of Egyptian magic would be crucial in the story. He is more reserved than Sadie but has a strong sense of duty. When paired with Percy, he could learn a lot about different ways of fighting and protecting, and his character growth as he adapts to working with demigods would be an interesting aspect of the fanfic.
Percy himself would be very interesting. He has all his demigod skills and his experiences always lead to some exciting situations. Just imagine him trying to have a normal beach vacation but then getting dragged into an underwater adventure by some sea - related mystery.
Another interesting interaction would be between Annabeth and Tony Stark. Annabeth is highly intelligent and strategic, much like Tony. They could either be in a battle of wits, constantly trying to one - up each other in terms of coming up with plans, or they could end up working together really well. Annabeth could teach Tony about ancient Greek architecture and strategy, while Tony could show her some of his latest high - tech inventions.
Grover from Percy Jackson would also be a fascinating crossover. His connection to nature and his ability to sense things that others can't would be really cool in the Twilight world. He could befriend the werewolves because of their connection to nature as well. And his generally nervous but loyal personality would add a different flavor to the interactions in the Twilight world.
In a 'Percy Jackson adopts Harry Potter' fanfic, the plot could start with Percy being on some kind of mission that crosses into the wizarding world. He stumbles upon Harry, who is alone and vulnerable. Percy decides to adopt Harry because he sees the same kind of determination and courage in Harry that he has. As they journey together, they exchange knowledge. Percy teaches Harry about Greek mythology and combat skills, while Harry shares his knowledge of magic. They form a bond that helps them face threats from both magical and mythological creatures, and they might even team up to fight against a common enemy that is a threat to both their worlds.