Another possibility is that they form an unlikely friendship. The Doctor could show Sherlock things he never thought possible, like different planets and time periods. Sherlock, in turn, could help the Doctor with his investigations on Earth, especially when it comes to human behavior. They might start to respect and rely on each other, and their combined adventures would be quite the story in fanfiction.
Well, in fanfiction, when Sherlock meets the Doctor, they might end up solving some extraordinary mystery together. Maybe they use Sherlock's deductive skills along with the Doctor's knowledge of the universe. For example, they could be in Victorian London and a strange alien entity shows up. Sherlock would notice the little details about the entity's behavior and appearance, while the Doctor would know what kind of alien it is and how to deal with it.
In this fanfiction, perhaps there is a mystery that spans different dimensions. Doctor Strange is familiar with the multiverse and different planes of existence, while Sherlock is an expert in solving mysteries in his own world. A series of disappearances start to occur, and the victims seem to be vanishing into thin air. Strange realizes that it has something to do with a portal between dimensions that has been misused. He teams up with Sherlock, who uses his sharp mind to figure out the pattern of the disappearances. Together, they close the portal and rescue the victims.
In this fanfiction, there could be an epic battle scenario. Maybe the Doctor's intelligence and unique abilities from his own universe could be pitted against the combined might of the Avengers. He might use his time - traveling skills to outwit the Avengers or team up with them to face a common enemy from another dimension.
In a 'Tenth Doctor meets Eleventh Doctor fanfiction', they might start by being a bit competitive. The Tenth Doctor could show off his sonic screwdriver skills, while the Eleventh Doctor would counter with his own unique way of using it. Maybe they'd end up teaming up to face a common enemy, like a powerful Dalek or a new kind of alien threat. They could also have some interesting conversations about their different experiences with their companions.
In the fanfiction, the 11th doctor, with his eccentric and energetic personality, could initially be a bit confused by the 13th doctor's more modern approach. But then they could start to combine their wits. For example, the 11th doctor's knowledge of ancient alien races could be paired with the 13th doctor's understanding of current galactic politics. They could work together to save a planet that is on the brink of destruction due to a complex web of time - related issues. The encounter could also lead to some humorous moments, like when they argue about who has the better sonic screwdriver or who has had the more exciting adventures.
They could also meet in a time - locked situation. The 12th Doctor is trying to solve a mystery from his past, and the 13th Doctor stumbles upon the same situation in her present. At first, they don't understand how they are both involved, but as they start to piece things together, they discover that it's all part of a much larger, more sinister plot. Along the way, they might meet some old friends or foes from their respective tenures as the Doctor. And in the end, they work together to outwit the mastermind behind the plot, all while having some really interesting conversations about their experiences as the Doctor.
In such a fanfiction, they might have an adventure together. Maybe they team up to fight a common enemy that neither could defeat alone. For example, a new, powerful alien threat that has emerged in the Doctor Who universe.
Neither might be fully dominant. They could end up being equal partners. Sherlock's deductive reasoning and the Doctor's knowledge of the cosmos could complement each other so well that they work side by side. They would respect each other's abilities and share the decision - making process. For instance, in a case where an alien is using human technology to cause chaos, Sherlock would analyze the human part of the situation while the Doctor figures out the alien technology involved, and they would jointly come up with a solution without one being clearly in charge over the other.
It could be a powerful sorcerer who has turned to the dark side. This sorcerer might be using his magic to manipulate events in Sherlock's world for his own gain. He could be creating illusions and false trails to throw Sherlock off, while also using his magic to fight against Doctor Strange.
In fanfiction, when the 13th Doctor meets the 11th Doctor, there could be a lot of chaos and fun. They might exchange stories about their adventures. Maybe they would team up to fight a common enemy that spans across their different timelines.
In fanfiction, when the 11th Doctor meets the 12th Doctor, there could be a clash of personalities at first. The 11th is so full of child - like wonder and the 12th is a bit more reserved. But then they might find common ground in their love for the TARDIS and for saving the universe. They could end up learning from each other. For example, the 11th Doctor might teach the 12th how to be more carefree sometimes, while the 12th Doctor could show the 11th how to be more strategic in dangerous situations.