Well, perhaps in some 'Harry Potter dimension jumper fanfiction', there's a dimension where the Marauders are still alive and they team up with the modern characters to fight a new dark threat. Or a dimension where magic is dying out and the jumper has to find the source of the problem and fix it. This could involve traveling to different magical locations in that dimension, like the Forbidden Forest which might hold some secrets.
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.
One idea could be that in the alternate dimension, Voldemort won the war and Hogwarts is now a dark and dreary place where students are taught only dark magic. Another could be that the wizarding world is merged with the Muggle world in a strange way, like there are magical creatures running amok in London streets. Or perhaps in this alternate dimension, Harry was sorted into Slytherin and has to deal with a whole different set of challenges and prejudices.
A really cool plot could be that the traveler goes to a dimension where magic is fading away. They discover that it's because of an ancient curse. So, they embark on a journey to find the origin of the curse and a way to break it, all while interacting with alternate versions of the well - known Harry Potter characters.
Another interesting aspect could be that in his personal dimension, Harry has a different set of friends. He might meet some students from other wizarding schools who are also in their own personal dimensions, and together they form a unique magical community.
One idea could be that in the alternate dimension, Voldemort won the war long ago. Hogwarts is now a dark and dreary place, with Death Eaters as teachers. Harry and his friends, who are part of an underground resistance, have to find a way to travel back in time to change the course of history.
Harry Potter himself is often still a popular character. Since it's a dimension jumper fanfiction, his character can be explored in different scenarios across dimensions. Hermione is also popular as she can use her intelligence to figure out the differences in each dimension.
One interesting aspect could be the unique crossovers it might feature. Since it's a jumper fanfiction, perhaps Harry Potter jumps into different and unexpected universes, which can bring fresh and exciting plotlines.
One interesting plotline could be a jumper that has special powers. For example, it might be able to transport the wearer to different magical locations in the Harry Potter universe. Another could be a jumper that changes its appearance based on the wearer's mood or the magical situation around them.
One possible interesting plot could be Harry finding a new magical dimension where the rules of magic are completely different. For example, instead of using wands, magic is controlled by thoughts alone. He has to learn these new ways quickly to face a dark threat that exists in this dimension which is planning to invade the wizarding world he knows.
One idea could be that Peter discovers he has special powers in this other dimension that he doesn't have in his own world. For example, he can control elements like fire or water. Another could be that he meets alternate versions of his friends and family, and has to deal with the differences in their personalities. Maybe in this dimension, his best friend is his enemy.