Another plotline could be that the immortal has some knowledge that the Doctor needs. The Doctor is constantly seeking knowledge, and the immortal, having lived for so long, might hold the key to solving a big problem in the universe. So the Doctor has to convince the immortal to share that knowledge, which might not be easy as the immortal could be very guarded about it.
A third plotline could involve the Doctor trying to understand the concept of immortality itself. He's seen many strange things, but immortality is still a complex idea. He might study the immortal, not in a cruel way, but just out of scientific curiosity. And in the process, they could form an unexpected bond as they get to know each other better.
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.
Perhaps they find themselves in a situation where they have to rescue a group of people trapped in a parallel universe. Jack's skills as a former Time Agent and the Doctor's ability to navigate difficult situations would be crucial in this rescue mission. It could also be a chance for them to learn more about each other's pasts and grow as characters.
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.
A storyline could involve a character from Torchwood getting trapped in a time loop. The 11th Doctor shows up and, with his knowledge of time mechanics, tries to break the loop. Along the way, he gets to know the Torchwood team better and they learn a great deal from him about the nature of time and the wider universe.
Well, they might have some really interesting conversations. The Doctor, with his vast knowledge of the universe, could be intrigued by the immortal's long - lived experiences. Maybe they'd team up to solve some sort of mystery that's been around for ages because of the immortal's long - term perspective and the Doctor's problem - solving skills.
Perhaps they would team up to fight some common enemies. Harry's magic and the Doctor's technology could be a great combination. They might travel through time and space together, with Harry using his magic to assist in situations where the Doctor's technology might not be enough, and vice versa. It would be really exciting to see how their different skills and knowledge would interact.
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.
One possible plotline could be the 11th Doctor and Rose exploring a new and mysterious planet together. They might encounter strange alien species and have to use their wits to survive. Another could be them reuniting after a long time apart and having to deal with the changes in their relationship. Maybe Rose has new skills or experiences that the Doctor has to get used to.
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.