There was an unproduced Doctor Who story called The Dark Dimension which would of taken place in an alternate universe where that Doctor never regenerated passed his 4th incarnation. It was to be a multi-Doctor story which would of also featured 3, 5, 6, and 7. The later Doctors would either be from the main universe since they don't exist yet in the Dark Dimension or they'd be from the future. Anyway the story is primarily focused on 4 who I assume travels with an alternate universe version of Ace.
Anyway I'm bringing this up because I'm curious. What if you were to write a Doctor Who story that takes place in an alternate universe. You can take any Doctor and extend that incarnation's life span beyond his normal years. How would you do it and what else would be different as a result of the Doctor regenerating at a different time.
What I would do is start with Utopia. Two TARDIS' arrive in Cardiff. One disguised as a Port-a-potty intercepts Jack Harkness before he can make it to the Doctor's TARDIS. Jack still ends up causing a TARDIS to travel to the end of the universe it's just not the Doctor's. The door to the Port-a-potty opens and Jack hears a mysterious voice call for him to come in. "I'm not sure why but my TARDIS doesn't seem to like you. Why is that?" He says while scanning Jack with his own Sonic Screwdriver. "Doctor? Is that you?" Asks Jack to the mysterious Time Lord. "I'm You from the Future." replies the Time Lord. "That's impossible you look nothing like me." Jack says in a tone that implies he thinks he's better looking but is trying to be nice and not actually say it. "No, my name is You and I'm from the future. I was introducing myself. You know we Time Lord get to pick our own names, I choose mine just so I could confuse people like that whenever I introduce myself." Jack gives this look like he's trying not to laugh. "Where's the Doctor, this was suppose to bring me to him not you." Jack holds out the container with the Doctor's severed hand inside it. "I could send out a signal to your friend's TARDIS using this to pin point his location." You hooks up a few wires from the main console to the hand container. "If this Doctor of yours is out there anywhere in time he should be able to follow that homing beacon and follow us here... Where ever here is."
After the Doctor arrives there's a discussion between him an You and how the Doctor thought he was the only Time Lord left. Oddly You never seems surprised and everyone seems to think that there's something he's not telling. Anyway, the rest of the story plays out pretty much the same. Except now after the Master steals the Doctor's TARDIS they can just follow him in You's TARDIS instead of using the Vortex Manipulator.
You would leave the story just before the Doctor gets his TARDIS back from the Master. At which point Jack would finally remember to actually tell the Doctor about the hand in the jar that is now in You's TARDIS.
Everything else after this point would pretty much stay the same as the main universe until we get to Journey's End where the Doctor regenerates into Matt Smith because he doesn't have the spare hand there to throw the excess regeneration energy into. As a result of this Doctor Donna wouldn't have happened either and there would be no Meta-Crisis Doctor to cross over into that alternate universe with Rose. Of course if Doctor Donna didn't happen then the Doctor would have no reason to erase her memory. I really don't like her but as a consequence of what I'm trying to do I suppose this means that she would continue to travel with the Doctor for his next few adventures. So everything after this would be slightly altered because of Matt Smith's Doctor being around earlier and Donna Noble continuing to travel when her main universe counterpart didn't.
You would return at the end of the Waters on Mars story. Just as the Doctor and Donna are about to leave You's TARDIS appears. You comes out as says "Doctor, I forgot to give this back to you before I left before." The Doctor takes his spare hand and responds "You didn't forget. Why would you pick this moment to finally bring it back, why would you leave the way you did in the first place. It all seems very planned." You struggles to come up with an answer. "Jack told me you said you were from the future. You know what's suppose to happen next don't you. You're trying to change history. You know I had some vanity issues in that last incarnation, if you hadn't stolen this before I wouldn't be here now would I? I'd still be him." You nervously finally comes out and admits it. "Oh right yes, I'm sorry. I tried to do this like it was all an accident but I intentionally went to Cardiff to stop Jack from meeting you there because I knew it was the only time I could get your hand. I always planned to return it to you at this moment right before you'd need it so you can regenerate and keep this face." A little puzzled the Doctor continues "I'd already figured that out, what I don't understand is why, why go through all this trouble?" You responds "Because you're my Doctor. You're the reason I stole a TARDIS, you're the reason I lived out all of my incarnations as an actor on Earth... had to play in a romantic comedy against myself once that was awkward, I even modeled my Sonic Screwdriver after yours... well you haven't got it yet and it's not exactly the same but you'll see soon, very soon." The Doctor responds "And what happens if I don't use this. What are you going to do then?" You explains "I'm not a threat to you Doctor but your next incarnation, he's the last. You will get another regeneration cycle but you need to stay as you are, she won't help him." You retreats into his TARDIS as the Doctor yells "What do you mean that? She who? What is my next incarnation like, why wouldn't she help him the same as she would me?"
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