One good crossover idea could be to have the characters from My Hero Academia attend the DWMA (Death Weapon Meister Academy) in the Soul Eater world. Imagine Deku trying to learn how to use a Death Scythe! It would be interesting to see how the different power systems interact. For example, quirks vs. the ability to turn into weapons and the use of soul wavelengths.
One idea could be that Kakashi is somehow transported to the My Hero Academia world. He could become a teacher at UA, using his ninja skills and wisdom to train the students in new and unique ways. His Sharingan would be a very interesting power in the MHA universe.
Perhaps in this crossover, the concept of the tailed beasts in Naruto are related to the Kishin in Soul Eater. The tailed beasts are seen as powerful and dangerous entities, much like the Kishin. A group of characters from both universes, including Naruto, Maka, and Soul, come together to find a way to either control or destroy these powerful forces that threaten both their worlds. They would have to learn from each other's strengths and weaknesses to succeed.
One idea could be that Godzilla arrives in the My Hero Academia world during a major villain attack. The heroes initially see Godzilla as a threat but soon realize that he is targeting the same villains who are causing environmental destruction. His massive size and power could be a game - changer in the battle.
A great fanfiction idea would be to have some of the My Hero Academia students train with Batman. He could teach them his stealth and combat techniques. This would be especially interesting for characters like Todoroki. Batman could also help them understand the importance of psychological warfare against villains. In addition, there could be a plot where a new villain emerges in the My Hero Academia world, and Batman has to use his knowledge of Gotham's villains to help the heroes figure out how to defeat this new threat.
A great crossover idea is with the Dragon Ball series. The powerful Saiyans could interact with the My Hero Academia characters. Goku could train the students at UA to reach new levels of power. Also, a crossover with the Attack on Titan world would be intense. The heroes would have to deal with Titans in a whole new way and use their quirks in that battle - filled environment.
There are quite a few great crossover fanfictions between Avengers and My Hero Academia. One that stands out involves the Avengers being transported to the My Hero Academia universe. In this story, they have to adapt to the world of quirks while also trying to find a way back home. It's really interesting to see how characters like Iron Man interact with the likes of All Might.
One idea could be a crossover with the Naruto universe. The characters from My Hero Academia could interact with Naruto characters. For example, Deku might learn some new fighting techniques from Naruto. Another idea is a crossover with the Harry Potter world. The students at U.A. could visit Hogwarts and experience magic, while the Hogwarts students could learn about quirks.
A cool My Hero Academia crossover fanfiction idea would be with the Avengers. The heroes from UA could team up with the Avengers to fight a common enemy. For example, a powerful villain who can absorb quirks and powers. It would be interesting to see how characters like All Might and Captain America interact, and how their leadership styles differ.
One idea could be to have the characters from BNHA attend the Death Weapon Meister Academy in the Soul Eater universe. They could learn about soul resonance and how to handle weapons in a whole new way. For example, Deku could be paired with a unique weapon and struggle to master the new techniques.
One idea could be having the characters from My Hero Academia participate in the Street Fighter tournament. For example, Deku could use his One For All power in the fighting matches. Another idea is a team - up between Ryu and All Might to fight a common enemy. Maybe they could face a villain who has the ability to steal powers, like All For One, but also has the combat skills of the toughest Street Fighter villains.