A cool plot could be that the dimension traveller gets stuck in a dimension where the events of the main story are repeating in a loop, but with slight differences each time. The traveller has to figure out how to break the loop while also dealing with the different versions of the characters they meet along the way. They might discover that a certain character's hidden potential in one loop is the key to breaking free.
One idea could be the dimension traveller arriving in a world where quirks are reversed. For example, heroes have villain - like quirks and vice versa. This would create a lot of chaos and interesting character interactions as the traveller tries to figure out how to navigate this strange new world.
I think All Might in his prime could be a great main character for this type of fanfiction. If he were to travel to different dimensions, he could spread his symbol of peace in new worlds. He would face different types of villains and heroes, and his experience and power would make for an exciting story. Plus, we could see how he adapts his hero style to different situations in various dimensions.
How about a fanfiction where the villains and heroes have to team up? There could be a greater threat, like an alien invasion or a powerful quirk - user who is out to destroy the entire world. The heroes and villains realize that they can't defeat this threat alone, so they put aside their differences. This would lead to some really interesting character interactions, like Bakugo having to work with Shigaraki and both of them learning to respect each other's skills despite their opposing natures.
Maybe a plot where a group of Warhammer heroes are sent to the Hero Academia world to stop a chaos invasion that is starting to seep into that realm. They have to work with the local heroes, sharing their knowledge of dark magic and ancient weapons to combat the new threat. This would involve a lot of cultural clashes and learning experiences between the two groups.
An interesting plot could involve an OC who is initially thought to be quirkless but discovers a latent quirk later on. This OC could then struggle to catch up with the others in terms of training and development. Or, an OC with a shapeshifting quirk could be used in a plot where they have to infiltrate a villain's lair by taking on the form of one of the villains' minions. They would have to be careful not to be discovered and also gather intelligence along the way.
An interesting plot could involve an anti - hero who has a hidden agenda that is not entirely evil but also not in line with the traditional hero goals. Maybe they are trying to expose a corrupt part of the hero society from within. They could form alliances with some villains who also have a vendetta against the corrupt elements. This would create a complex web of relationships and moral dilemmas.
One plot idea could be a villain who is secretly a double agent, working for the heroes all along. They infiltrate the villain group and gather information. Another idea is a hero who loses their quirk and has to rely on their wits and combat skills alone, like Batman in the DC universe. And a villain - hero team - up to face a greater threat that neither can handle alone.
One idea could be a crossover where the students from Little Witch Academia visit UA High. They could participate in a joint training exercise. The witches could use their magic in creative ways during combat scenarios, while the heroes-in-training show off their quirks. It would be a fun mix of different powers and personalities.
One idea could be a 'what if' scenario where the villains and heroes have to team up against an even greater threat from another dimension. It would be fun to see how characters like Bakugo and Dabi interact in this forced alliance.
One idea could be that during Halloween, the villains use the spooky season as a cover to carry out a major heist. The heroes have to figure out their plan while also dealing with all the Halloween chaos in the city. For example, there could be trick - or - treaters getting in the way and the villains using Halloween decorations to hide their traps.
One idea could be reincarnating as a minor villain and trying to reform. For example, using knowledge of the future to avoid getting caught up in big evil plans. Another could be reincarnating as a quirkless student but finding a unique way to be a hero, like developing amazing combat skills without a quirk. Maybe reincarnating as a side character and becoming the mentor to the main heroes, guiding them with knowledge from the original story.