Perhaps a group of rogue time - traveling wizards. They come from a future in this dimension where the wizarding world has been destroyed, and they believe that changing the past (even if it means causing chaos) is the only way to save their future. They see Harry as a threat to their plans because he has a natural inclination to preserve the present order.
He could also meet some sort of dark wizard or villain that is even more powerful than Voldemort in this new world. This would pose a great threat to Harry and force him to use all of his skills and knowledge, both from his own world and what he's learned in the new one, to defeat the enemy.
Well, perhaps Percy could find himself in a dimension where the laws of physics are completely different. He might have to learn new ways to use his powers. For example, if water behaves strangely there, like it's solid in some areas and gas in others, he'd have to adapt quickly.
Well, a cool plot for 'Harry Potter in Another Dimension' fanfic could be that Harry discovers he has a twin in this other dimension. His twin has been raised by Voldemort and has a very different view of the wizarding world. Harry has to find a way to convince his twin to abandon Voldemort's ways. Or, what if in this dimension, the Sorting Hat can talk out loud all the time and gives very different sorting decisions? For example, it might put all the brave students in Slytherin and the cunning ones in Gryffindor. It would be really interesting to explore how the relationships between the houses change.
Well, in Harry Potter fanfiction, the 'Dimension Father' might be a character with a very specific role. Maybe he's a sort of guardian of the dimensional boundaries. He ensures that no dark magic from other dimensions seeps into the main Harry Potter universe. He could also be a source of knowledge for characters like Hermione who are always eager to learn new magic. For instance, he might teach her about the spells and incantations that are unique to other dimensions, which she could then use to help Harry in his fight against the dark forces.
Perhaps he'll come across a powerful wizard or witch who is the ruler of that dimension. This character could be either benevolent or malevolent, and would surely have a great impact on Harry's adventure in that dimension. They might try to use Harry for their own purposes or help him return to his own dimension.
Well, he could face a whole new set of challenges. Maybe the magic there works differently. For example, spells he uses on Earth might not have the same effect, or he could encounter a powerful dark force that he has to figure out how to defeat without the help of his usual Hogwarts friends and professors. He'd have to rely on his own wits and the skills he's learned over the years to survive and overcome difficulties.
Maybe he'll have to learn a whole new type of magic. In the other world, the rules of magic could be completely different. Instead of using wands, they might use their minds directly to cast spells. So Harry would have to adapt quickly to survive and figure out how to use this new magic system.
Well, he might make new friends. In a different school, there could be new magical traditions and spells for him to learn. He'd also face different challenges compared to Hogwarts.