Before I start this, you might want to have a read of this link here where they explain each of the different dimensions that we can comprehend.
I believe I read that there's supposedly an 11th and 12th dimension beyond 10, but we only need the first 6 here...
There have been stories in the past where we've had 'The X doctors' - they find a reason to have the doctors from various times all come together to solve a specific problem.
I imagine an episode where The Tardis is pulled out of regular space time, and into a difficult to comprehend, 6th dimensional structure that in this instance looks suspiciously like an empty village hall.
DC Comics have a similar concept with their Multiverse. You sometimes find there's a place where far larger beings are able to oversee the 'multiverse' and travel between instances of each world by dipping in and out of the third dimension as and when they please.
In that it tends to look more like a laboratory, but it could be anything.
The new Doctor and her assistant find themselves in this mind bending situation, where she is completely out of her comfort zone and has gone further than ever before.
She has been pulled there by The Master...but he died...and was evil...what's going on?
The Master introduces Missy, and a handful of alternative doctors, and masters, and assistants, and explains that none of them are 'the' people The Doctor knows them as, they're people from another universe entirely.
The Doctor has some experience of this from when Rose ended up in a different Universe but that's 5th dimensional business which only goes one way and is for the most part 'similar' to the world where The Doctor started.
This time things are much bigger than that. These worlds have seen huge changes that are so far adrift from 'our' world, that she is talking to Doctors who watched The Daleks win in various wars, or The Cybermen assimilate Earth, they're still fighting the good fight.
This story would be an opportunity for all 13 doctors to be represented, along with any other additional alternate reality doctors that they wanted to include for a 'special' episode.
They could even include 'future' doctors that remember 'being' the current doctor and the adventures she has had.
Being a 4th dimensional being, not all doctors will be the same age at this moment in time, they're time travellers, there'd be no telling how old each one was because some could've survived as the 1st Doctor for 10,000 years while others were on their 17th incarnation after a decade due to recklessness and extremely bad luck.
An army of doctors, masters, assistants, K9s and everything else are being brought together to address a threat that is bolder than any they've attempted before.
In one universe, at one moment in time, the Doctor...gave up.
This doesn't happen lightly, in fact there hasn't been a single record throughout all of history, across every known universe, of this happening, but somehow, somewhere, it finally has.
Infinite universes have created a single instance in time and space and where things aligned so specifically that The Doctor has conceded.
The result is horrific.
The major races that have fought the doctor time after time are taking chunks out of the universe, enslaving entire galaxies and going to war with one another.
Alliances are being forged, as Cybermen indoctrinate every living creature, and Daleks exterminate their way through worlds.
We end up with Cyber Silurians, Cyber Ice Warriors, Cyber Sontarans, Weeping Angels, you name it, they're all being amalgamated into a progressively evil empire.
The tidal wave of brutality has no limits. With all of time and space at their mercy there comes a point in time where there are no more worlds left to conquer.
It is at this point that the threat is beginning to become a concern across the multiverse, and the Doctor's compatriots have been summoned to try and put a lid on things before they figure out how to divert their attentions towards the fifth and sixth dimensions and beyond.
The Master wants to utilise a plan to eliminate the currently overrun world, by merging it in to a world in the 7th dimension where the universal laws of physics would be completely different, and therefore in theory, no life (mechanical or otherwise) could exist.
That would wipe out the threat in one foul swoop.
Most of The Doctors, especially our very own, are pained at the thought of effectively murdering an entire universe, to protect every other universe.
The needs of the many outweigh the needs of the few. But a universe of lives?
Is it fair to destroy any species, let alone every remaining species, because their instincts are to kill and assimilate?
If Lions were a more dominant species and decided to hunt and kill every other living thing in their path for food and resources, would that warrant wiping them out?
Humans have spread far and wide across every stretch of many universes, and yet no-one considers their rampant consumption worthy of extinction.
There is always a dominant species, and that dominant species always ends up bending the universe to their will.
This time it just happens to be everything that The Doctor has ever worked to prevent.
It goes without saying that the universe needs to be contained, it needs to be diffused.
But wiping out anything for simply following its instincts is a dodgy path that The Doctor is not prepared to walk down.
So instead, The Doctor has to propose a plan.
A mixed group of characters are drafted to visit the overrun 'dark' universe alongside our Doctor, whilst The Master sets plans in motion to destroy the universe the moment things look like they're about to spiral out of control.
The Doctor finds herself in a situation where she is trying to rescue beings who would kill her on site given half a chance.
Whilst racing against the clock to avoid the destruction of the universe, preventing the threat to the multiverse, and ultimately preventing her own death and the deaths of her new companions.
Unfortunately, I'm at 1000 words and couldn't possibly finish this tonight.
Let me know what you think so far in the comments!