One idea could be a character going back in time to prevent a major villain's origin. For example, if someone went back to stop All for One from corrupting Tomura Shigaraki as a child. Another plot could involve a hero traveling to the future to see the outcome of their current actions and then coming back to make changes. Maybe a student like Izuku Midoriya goes to a future where the heroes have lost and tries to change the present to avoid that fate.
Maybe Ladybug's Miraculous gets mixed up with an MHA student's Quirk. So the student starts to exhibit powers related to both the Miraculous and their original Quirk. This could lead to some really cool fight scenes where they have to learn to control these new combined powers. They might also face challenges as the other characters in both universes are skeptical about this new power combination.
A cool plot might be that the Hogwarts students attend U.A. High School. Hermione would surely excel in academic subjects there, while Ron could struggle a bit more. And Harry could use his experience with fighting dark magic to help in hero training. They could also introduce magic - based quirks to the MHA world, which would change the dynamic of how heroics are done.
One idea could be that the Avengers are somehow transported to the MHA universe. They have to deal with quirks while also trying to find a way back home. Maybe they team up with the students at UA to fight a common villain who has a power that combines both advanced technology and a powerful quirk.
One idea could be that Naruto characters visit the MHA world and have to adapt to the modern society and different power system. For example, Naruto might be intrigued by how quirks work compared to chakra. Another plot could involve villains from both universes teaming up, forcing the heroes from Naruto and MHA to collaborate. They would need to combine their unique fighting styles and powers to defeat the combined threat.
One idea could be that the heroes from MHA are transported to the Super Sentai world and have to team up with the Sentai warriors to fight a common enemy that is threatening both universes. Maybe a powerful villain has found a way to cross dimensions and is causing chaos.
Another possibility is a crossover with the world of Naruto. The characters from MHA could participate in the Chunin Exams. Bakugo might be really into showing off his skills in this new and different kind of competition.
One interesting idea is the crossovers between different characters from the MHA universe and other universes. For example, seeing Deku interact with characters from other popular anime like Naruto or One Piece can create really unique and exciting storylines.
One idea could be Yoda traveling back in time to train Anakin Skywalker differently, thus preventing his fall to the dark side. Maybe he goes back to the very beginning of the Jedi Order to gain more knowledge about the Force and bring it back to his own time.
One idea could be Shinji traveling back in time to prevent the Second Impact. He might try to change the actions of his father that led to it. Another could be Asuka traveling to a future where the Evangelions have been completely forgotten and she has to figure out how to get back to her own time.
Another plot could be a character from the future coming back to the present in Shameless. They could be trying to stop a future disaster that is somehow linked to the Gallagher family. This would involve a lot of mystery and intrigue as they try to figure out what the future event is and how to prevent it while dealing with the chaos of the present - day Gallagher family.