Perhaps the plot could start with Percy being sent to Hogwarts for some reason, like his demigod powers are being affected by some dark magic that only the wizards can help with. While at Hogwarts, he uncovers that he is Dumbledore's grandson. This leads to a whole series of events where he has to deal with the Hogwarts politics, make friends and enemies, and also figure out how to use his demigod and new - found wizarding heritage to stop an ancient evil that is starting to rise again. He could face challenges like dealing with the Slytherin students who might be jealous of his connection to Dumbledore, and also trying to convince the demigod world that the wizarding world can be an ally.
The plot could revolve around a new threat that targets both the demigod world and the wizarding world. Percy, as Dumbledore's grandson, feels a responsibility to bring the two worlds together to fight this threat. He could start by gathering a group of his friends from both worlds, like some of his demigod friends and some Hogwarts students he befriends. They would have to learn to work together, with Percy acting as a bridge between their different powers and cultures. Along the way, Percy might also discover some long - lost secrets about his family and the two worlds' connection.
One possible plot could be Percy discovering his relation to Dumbledore. Maybe he starts having strange dreams or visions that lead him to the wizarding world. He then has to learn about his new family connection while also trying to keep his demigod identity a secret from most of the wizards, as they might not understand it.