A plot could involve a powerful dark force that is threatening both universes. Hermione's intelligence and knowledge of ancient magic and Doctor Strange's mastery of the mystic arts would make them a great team. Maybe the dark force is stealing magic from both worlds and they have to track it down across different dimensions. They start by comparing notes on different types of magic they know and find a way to combine their powers to combat the threat.
One idea could be that a magical rift opens up between the Harry Potter universe and the Marvel universe where Hermione and Doctor Strange meet. They could team up to close the rift which is causing chaos in both worlds. Strange uses his magic to hold off the magical creatures spilling into the Marvel world while Hermione uses her vast knowledge of spells to find a way to close it from her side.
Perhaps there is a prophecy in both universes about a person from another world coming to save them. Hermione accidentally gets transported to the Marvel universe and is mistaken for this savior. Doctor Strange realizes she is from another world and decides to help her get back home while also using her knowledge to fight an upcoming evil. Along the way, they learn from each other's magical techniques and develop a friendship.
One idea could be that Doctor Strange somehow gets transported to the RWBY universe. Maybe he's there to help deal with a powerful Grimm that has magic - like abilities that the normal Huntsmen and Huntresses can't handle. He could use his magic to teach the RWBY characters new ways of fighting and also learn a thing or two from them about their unique combat styles.
One idea could be that Doctor Strange accidentally opens a portal to the wizarding world of Harry Potter. He could end up at Hogwarts and be mistaken for a new kind of wizard. Maybe he tries to use his magic to teach the students some new spells or ways of magic, but it causes chaos because his magic is so different from theirs. For example, his use of the Time Stone could mess with the time - turners at Hogwarts.
Perhaps a fanfiction where Doctor Strange loses his powers and has to rely on his wits and the knowledge of ancient spells he has memorized to defeat a powerful enemy. This would show his growth not just as a sorcerer but as a person. For example, he could use his medical knowledge in combination with some basic magical principles to outsmart the foe.
One idea could be a crossover with 'Grey's Anatomy'. The Good Doctor's Dr. Shaun Murphy could visit Grey Sloan Memorial Hospital. He could collaborate with the doctors there on a complex surgical case. Maybe there's a patient with a very rare condition that requires Shaun's unique perspective and the surgical skills of the Grey's doctors like Meredith Grey.
One idea could be Doctor Strange accidentally sends the Avengers into an alternate dimension where magic doesn't exist and they have to find a way back using only their non - magical skills. Another could be that an ancient evil forces Doctor Strange to choose between sacrificing the Avengers or the entire world. Or perhaps a spell gone wrong makes the Avengers swap powers with each other, and Doctor Strange has to fix it while also dealing with an incoming threat.
Some possible plot ideas include Hermione being mistaken for a powerful Grounder because of her magic. She could then use this to her advantage to broker peace between the different factions. Or maybe she discovers a magical element in The 100's world that she didn't expect, like a magical artifact left over from a pre - apocalyptic civilization. This could lead to a race among the different groups to obtain it, with Hermione in the middle trying to ensure it's used for good.
One idea could be that the Avengers need Doctor Strange's help to enter an alternate dimension to retrieve a powerful artifact before the bad guys do. Strange uses his magic to create portals for the Avengers, but they face various challenges in the new dimension, like strange creatures and mind - bending illusions.
One idea could be that they team up to face a new, powerful interdimensional threat that neither can handle alone. Maybe a villain has found a way to merge different dimensions in a chaotic way, and Iron Man's tech and Doctor Strange's magic are needed to stop it.
One idea could be that you insert yourself as a new apprentice to Doctor Strange. You could start with little magical knowledge and learn from him, facing challenges like protecting the Sanctum Santorum from minor demons. Another could be that you are inserted into the story during the time when Strange is facing a powerful enemy and your unique modern - world knowledge helps him in an unexpected way, like using technology to enhance a spell.
One idea could be that Doctor Strange discovers he is pregnant due to some strange magical experiment gone wrong. His powers start to fluctuate in unexpected ways as his body adjusts to the pregnancy. He has to deal with the reactions of his fellow sorcerers, some of whom are shocked and others who try to help him manage his new condition while still protecting the world from magical threats.