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.
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 that Sherlock's deductive skills are needed to solve a mystery in the magical world of Doctor Strange. Maybe a powerful artifact has been stolen and Sherlock's unique way of seeing details helps find it. Another could be that Doctor Strange uses his magic to transport Sherlock to different dimensions to solve a case that spans across realities. For example, a serial killer who can move between dimensions and Sherlock has to use Strange's magic to track him down.
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.
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 in a magical - modern world setting. Maybe Hermione's magic causes some chaos in Jake's world. For example, her spells accidentally disrupt the technology in Jake's town. Another plot could involve them teaming up to solve a mystery that spans both their worlds, like a magical artifact that has ended up in Jake's modern world and is causing strange events.
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.
The 'Doctor Strange Crossover Fanfiction' that pairs him with the Guardians of the Galaxy is also a lot of fun. Strange finds himself in the middle of their wacky adventures in space. His serious and mysterious nature contrasts with the Guardians' more laid - back and comical personalities. There are some really humorous exchanges between them as they try to work together to stop an intergalactic threat.
Well, perhaps Hermione is sent to the 'Vampire Diaries' world to retrieve a powerful magical artifact that has somehow ended up there. Along the way, she meets Damon and Stefan. She forms an unlikely friendship with them as they help her search for the artifact. In return, she uses her magic to protect them from some of the more dangerous supernatural threats in their world.