You can start by looking on fanfiction platforms like Archive of Our Own (AO3). It has a large collection of batfamily fanfictions, including those involving dimension travel. Just use the search function and type in relevant keywords like 'batfamily dimension travel'. Another option is FanFiction.net, which also has a decent number of such stories.
A very popular plot device is the existence of parallel universes within the Batfamily context. Writers often explore what would happen if a key event in the Batfamily's history was different in another dimension. For instance, what if Jason Todd never died in one dimension? This allows for a lot of character exploration and interesting interactions between different versions of the characters. Also, the idea of a 'dimensional rift' that the Batfamily has to close before it causes chaos is quite common.
A popular 'Batfamily Time Travel Fanfiction' is 'Time - Bound Heroes'. This story has the Batfamily traveling through time to prevent a villain from changing key events in Gotham's past. The author does a great job of showing how each member of the family uses their unique skills in different time periods. There's also 'Chronal Chaos' which is a wild ride. The family gets scattered across time and has to find a way back together while also dealing with the consequences of their time - travels on the present - day Gotham.
Well, Batman is an obvious choice. He has the resources, the intelligence, and the motivation to venture into other dimensions. If there's a threat in another dimension that could potentially affect Gotham, he'd be there. Harley Quinn could also be a character who gets involved in dimension travel. Maybe she's chasing after the Joker who has somehow ended up in another dimension. And Oracle, with her technological expertise, could accidentally stumble upon dimension - traveling technology and end up in a different dimension while trying to fix or improve it.
One common trope is the 'fish - out - of - water' situation. When the Batfamily travels to a different time, they often struggle to adapt to the new era's technology, social norms, and culture. For example, in some fics, they go back to a time before smartphones and have to figure out how to communicate and gather information without modern tech. Another popular trope is 'fixing the past'. They might go back to prevent a tragedy or change an event that had a negative impact on the Batfamily in the present.
Dimension travel in Harry Potter fanfiction is really exciting. Sometimes, it allows the main characters to gain new powers or knowledge from other dimensions. They might meet alternate versions of themselves or their friends. It can also be a way to fix things that went wrong in their original dimension. For instance, if a character made a big mistake, they could travel to a dimension where that mistake didn't happen and learn how to correct it in their own world.
I really like the fanfiction 'Superboy in the Strange Dimensions'. In this story, Superboy discovers dimensions where the laws of physics are completely different. It's a fascinating read as he tries to adapt and use his powers in these new environments. There are also some great character interactions that add depth to the story.
One possible fanfiction could be about Naruko traveling to different dimensions in the Naruto universe and meeting alternate versions of her friends and enemies. She might learn new jutsus or gain unique powers from these encounters.
One great 'Dimension Travel Naruto Fanfiction' is 'A New Path in Another World'. In this fic, Naruto gets transported to a different dimension where the ninja world has some unique and strange rules. It's really interesting to see how he adapts his skills to this new environment.
Well, in a 'batfamily meets reverse batfamily fanfiction', a lot of character development could occur. The members of the regular Batfamily would have to re - evaluate their own beliefs and methods when confronted with their opposites. Maybe they would start to question if there's a thin line between heroism and villainy. And the reverse Batfamily might also experience some changes, perhaps seeing a different path they could take from interacting with the 'good' Batfamily.