Well, in a 'Harry Potter raised DC crossover fanfiction', perhaps Harry is raised by Wonder Woman. He could grow up learning about Amazonian values along with his own magical heritage. His magic might be seen as a new form of power in the DC world. For example, he could use magic to create protective shields during battles against the forces of Ares. Or he could be raised by the Flash, and use his magic to help the Flash with time - related problems, like creating a time - freezing spell to stop a time - traveling villain.
One idea could be that Harry Potter and his friends are transported to the DC Comics universe. They could team up with the Justice League to fight a common enemy like Voldemort who has somehow gained powers from a DC Comics villain. For example, Voldemort could have made a deal with Darkseid to gain more power in exchange for helping him conquer the wizarding world first. Then, Harry and the likes of Superman, Batman, and Wonder Woman would have to combine their magical and super powers to stop them.
One interesting plot could be how Harry's magical abilities are perceived in a world of nations. Maybe he uses his magic to solve international disputes. Another idea is that different nations try to influence his upbringing, each adding their own cultural and magical elements to his training.
One idea could be that Harry grows up with cat - like reflexes and stealth. He might be able to move around Hogwarts unnoticed more easily, like a cat prowling in the shadows.
In the fanfiction, it could be interesting if Harry uses his magic to protect the other orphans from bullies. He might not fully understand his powers yet, but his instincts kick in. And then when he finally gets his Hogwarts letter, the other orphans are both sad to see him go but also excited for him, and he has to figure out how to leave the only home he's known while also being eager to enter the wizarding world.
One idea could be that Harry Potter and some of his friends are transported to the DC universe and they have to team up with superheroes to fight a common enemy. Along the way, they form a unique bond with the DC characters, creating a harem - like group where everyone has different skills and personalities that complement each other.
Another plot could involve Gohan being mistaken for a new metahuman in the DC universe. As he tries to find his way back home, he gets caught up in a conflict between the Justice League and a group of supervillains. His Saiyan powers could be the key to resolving the situation.
One idea could be Goku ending up in the DC universe and having a friendly spar with Superman. Their different power sources and fighting styles would make for an exciting encounter. Maybe Goku learns about Kryptonite and how it affects Superman, which gives him a new perspective on weaknesses.
One idea could be Wolverine getting transported to the DC universe and teaming up with Batman. They could combine their detective skills to solve a mystery that involves both mutants and metahumans. For example, a new villain is creating chaos in Gotham by using some sort of technology that affects Wolverine's healing factor in strange ways.
One idea could be the Boys teaming up with a DC hero like Superman, but then realizing his 'good guy' image might be a facade too. Another could be Homelander facing off against Batman in a battle of wits and power.
One interesting plot idea could be that Snape, in raising Harry, teaches him advanced potions from a very young age. Harry becomes a prodigy in potions, much to the surprise of the other Hogwarts students. Another idea is that Snape's strict but fair upbringing makes Harry more reserved and less impulsive, which changes the way he interacts with his friends. He might be more cautious and calculating in his actions, especially when dealing with enemies like Voldemort.