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.
Another idea is that Kakashi is from a secret ninja organization in the MHA world. He is sent to UA to observe and potentially recruit students with special skills for his organization. This could lead to some interesting interactions between the ninja and hero cultures.
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 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.
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 interesting idea could be a crossover with another popular superhero universe, like Marvel or DC. This could lead to epic battles between different types of heroes. Another idea might be a crossover within the My Hero Academia world itself, for example, different classes or generations of heroes teaming up in unexpected ways.
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.
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.
One great crossover could be Kakashi training the students at U.A. High School. He could introduce them to new forms of combat and stealth techniques from the ninja world. Another could be a story where Kakashi teams up with All Might. Their different power levels and personalities would create an interesting dynamic. All Might's big - hearted heroism combined with Kakashi's more reserved and calculating nature would be a great contrast.
One cool quirk idea could be 'Shadow Mimicry'. The user can blend into any shadow and move freely within the shadow realm, also being able to mimic the actions of those whose shadows they are in. It gives a lot of stealth and surprise attack possibilities in a fanfiction.
One great 'My Hero Academia' crossover fanfiction is the one where they cross over with 'One Piece'. It combines the unique powers of the 'My Hero Academia' world with the adventurous and diverse world of 'One Piece'. The characters interact in really interesting ways, like Midoriya being amazed by Luffy's Devil Fruit powers and Luffy being intrigued by the concept of Quirks.