Maybe Harry realizes he made some mistakes in his past and decides to go back in time to correct them. He could try to save his loved ones who died in the original story.
In this fanfic, Harry might use his knowledge of the future to avoid certain dangerous situations. He could also work on improving the wizarding world from an earlier stage, like trying to make Hogwarts a more inclusive place right from the start.
It could be that Harry wants to change his relationships. For example, he might try to befriend some people he had misunderstandings with before. He could also focus on his studies more and become an even better wizard earlier in his new life.
Voldemort would still be a crucial character. Since Harry is redoing his life, he might try to defeat Voldemort in a more strategic and less dangerous way. Other characters like the Weasley family, who were always there for Harry, would be involved too. They could be part of Harry's new support system in his redone life.
It could be that his parents were trying to protect Harry in a really messed - up way. They might have thought that by 'betraying' him, like sending him away or making him seem like an outcast, they could keep him safe from a much greater threat. Maybe they knew some prophecy about Harry and thought this was the only way to ensure his survival. They might have made a deal with some dark force, believing they could outwit it in the end but ended up being seen as traitors by Harry and others.
Well, perhaps the grandfather could be teaching Harry all kinds of magic that his parents didn't have the chance to. He might introduce Harry to a different side of the wizarding world, full of old family secrets and forgotten spells.
One interesting plotline could be Harry using his knowledge from his first life to prevent certain tragedies. For example, he might be able to save Sirius Black much earlier by being more cautious about the events at the Ministry of Magic. Another could be him changing his relationships with his classmates. He might befriend Draco Malfoy in a different way, perhaps by reaching out to him and understanding his family situation better, which could lead to a very different dynamic at Hogwarts.
One possibility is that Percy relives his life and focuses on training more intensively. He could learn new skills or magic earlier, which would change the course of his adventures. Maybe he would be more strategic in battles, and as a result, save more people and gain more respect in the demigod community.
One interesting plot twist could be that Percy discovers a hidden power within himself much earlier. Since he already has the experience of his first life, he might be more in tune with his demigod abilities. Another twist could be that he decides to side with different gods in the power struggles, changing the whole political landscape of the demigod world.
Maybe Harry is a thief to steal back something important that was taken from him or his family. For example, a magical heirloom that has been wrongfully confiscated.
Perhaps Harry is given the task of mentoring some young Ravenclaw students. As he spends time with them, he starts to appreciate the values of Ravenclaw more. He might learn from them as much as he teaches them, and this could lead to new friendships and a different perspective on the Hogwarts houses in general. Along the way, they could face challenges together, like dealing with a new dark magic threat that targets Ravenclaw specifically.
Maybe Harry becomes an assistant to the doctor and they go on adventures through time and space. They might encounter various alien species and solve mysteries together.
Perhaps Harry's godmother is a bit of an eccentric and she believes that lemons are a key to unlocking an ancient magic related to Harry's family. She could be constantly experimenting with different lemon - based concoctions. And she might take Harry on a journey to find the rarest lemon in the wizarding world to complete a spell that will help him defeat Voldemort once and for all.