A fanfiction could also explore a situation where Dr. Strange accidentally ends up in the Harry Potter universe. Hermione is the first to discover him and she tries to help him get back. In the process, they exchange knowledge about their respective magical systems and form an unlikely friendship that changes the way they view magic.
One idea could be a crossover where Hermione's magic from the wizarding world and Dr. Strange's mystic arts collide. Maybe they meet in a dimension where both their forms of magic are being threatened and they have to combine their knowledge to save it.
Another interesting concept could be a fanfiction where Hermione travels to the Marvel universe and becomes Dr. Strange's apprentice. She brings her unique understanding of magic theory, which is different from the mystic arts, and they learn from each other, creating new spells and techniques together.
One idea could be an OC who is a time - traveling apprentice of Dr Strange. They could come from a future where magic has been corrupted and they travel back in time to learn from Strange and prevent the corruption.
One idea could be a what - if scenario. What if Strange and Christine had a moment of passion during a time - traveling adventure? Maybe they kiss in a parallel universe where they're not bound by the normal rules of their relationship in the main MCU timeline.
One idea could be that a magical anomaly brings Harry Potter to the world of Dr Strange. Harry, with his unique magical knowledge from Hogwarts, could team up with Dr Strange to fight a new dark force that is threatening both their realms. Their different styles of magic would make for an interesting dynamic as they learn from each other.
A really interesting plot idea could be that Strange's magic starts to seep into the My Hero Academia world, causing some quirks to mutate in unexpected ways. Maybe a character like Todoroki suddenly has his fire and ice powers combined in a new, magical way because of the influence. Another idea is that the Infinity Stones somehow end up in the My Hero Academia universe and the heroes have to figure out how to keep them safe from villains.
One idea could be a story where Dr. Strange's daughter discovers her own magical abilities in secret. Maybe she stumbles upon an ancient spellbook in the Sanctum Sanctorum and starts to practice magic on her own, without her father's knowledge at first.
I'm sorry, I don't have specific fanfiction stories to recommend off - hand. However, you can try searching on popular fanfiction websites like Archive of Our Own (AO3). Just type in 'hermione and dr strange' in the search bar and you'll likely find a variety of stories.
One plot idea could be that Dr Strange discovers a prophecy that predicts the end of the magical world. To prevent this, he must rewrite the stars, which means he has to find a way to change the fated events. He embarks on a journey through different dimensions to find the key to rewriting the stars, facing various magical creatures and challenges along the way.
One idea could be that Dr Strange senses a dark magical threat to Peter Parker. Tony Stark, being Peter's mentor, teams up with Dr Strange to protect him. They have to combine their scientific knowledge and magic to defeat the enemy.
One idea could be that they have to team up to solve a multiverse - related mystery. Their different magical and technological skills complement each other. For example, Dr Strange's magic can open portals to different dimensions, and Tony's tech can analyze the strange energy signatures they find there.
It might not be a traditional or 'legitimate' in the sense of being part of the original canons. But in the realm of fanfiction, it's a great idea. Fanfiction is all about creativity and mashing up different universes. Harry Potter has its own set of magic rules and Doctor Strange has his. Blending them could result in a whole new set of magic spells and powers that could be really cool to explore.