Whump fanfiction about the 13th Doctor often explores the more vulnerable and difficult situations the character gets into. It can show her facing powerful enemies alone, or dealing with personal traumas. For example, she might be injured in a battle against a new alien threat and have to struggle to survive while also protecting her companions.
Another trope is 'captivity'. Writers might have the Doctor captured by an evil alien race. During her captivity, she has to endure various forms of torture or interrogation, which tests her mental and physical strength. This trope allows for a lot of character development as she tries to outwit her captors.
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 some fanfictions, the 10th and 11th Doctor are brought together by a time anomaly. They are forced to cooperate to fix it, and along the way, they encounter old friends and enemies. The contrast between the 10th's more traditional style and the 11th's more zany approach creates interesting dynamics. They might also have to deal with the consequences of their previous actions in different timelines, which adds an extra layer of complexity to the story.
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.
It could be the Daleks. They are a classic Doctor Who villain. They might see the meeting of two Doctors as a threat to their plans for universal domination and try to stop it.
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.
One possible plot twist could be that they find out they are both parts of a larger plan by an unknown enemy. Maybe an ancient force has been manipulating their timelines to bring them together for some sinister purpose.
One possible plotline is that they meet in a time - locked situation. They have to work together to break the time lock. Another could be that they meet because of a shared enemy that has somehow found a way to target both of their timelines. They would then have to put aside their differences and use their individual strengths to defeat the enemy.