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, in this fanfiction, there could be a lot of exciting crossovers. Maybe the Torchwood team and the 11th Doctor team up to fight some new and powerful alien threats. They might share their different technologies and knowledge. For example, the Doctor's TARDIS could be used in a new way with Torchwood's high - tech equipment.
Well, there could be all sorts of adventures. Maybe they'd team up to fight a new alien threat that neither could handle alone. The Doctor's wacky and brilliant ideas combined with Torchwood's more grounded, Earth - based tactics could make for some really interesting scenarios.
The main characters would surely include the 11th Doctor. He would bring his TARDIS, sonic screwdriver and all his time - lord knowledge into the mix. From Torchwood, Toshiko Sato could be a significant character. Her expertise in technology and her rather shy yet intelligent personality could add depth to the story. She could potentially help the Doctor with some of his more complex technological problems, and in return, the Doctor could expose her to things she had only dreamed of in her scientific pursuits.
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.
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.
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.
Well, of course, the Doctor is always a popular focus. But from Torchwood, Toshiko Sato is quite interesting. Her technological expertise could be very useful when combined with the Doctor's knowledge. She could also learn a great deal from him. Another character that can't be ignored is Martha Jones. Although she has her own story with the Doctor, when she gets involved with Torchwood in the fanfiction, her medical skills and her past experiences with the Doctor can create a whole new set of storylines and character relationships.
One idea could be that they team up to face a new alien threat that is beyond what either of them has faced alone. Maybe an alien that can manipulate time in ways that disrupt the fabric of reality. Another could be a story where the Doctor and the Torchwood team have a clash of ideologies at first regarding how to handle a situation with a lost alien civilization on Earth, but then they learn from each other.
The key elements could include interactions between the characters from both shows, maybe a shared adventure or a mission to save the universe. Storylines could involve time travel paradoxes or facing a common enemy.
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.