Yes.
I can see the first episode of S12 now:
The Whitterer comes up against Missy. There's a tussle or sorts, and some space rays are involved. Anyway, long story short, they swap bodies and Gomez becomes the Doctor. The Whitterer becomes The Master, or Missy if you like, but is immediately killed by a tricky bout of Venusian flu. Regenerates into a cranky old man who immediately kills the 'Fam'. Fat Nan returns from the Netherworld in outrage but too is immediately killed before the police can query what she was doing up the tower that night. Cranky Master then breaks the fourth wall and, in a TV first, kills Chibbers with the death ray thing that used to make people really small. Not much power needed this time though, as he's already small, in artistic stature.
Gomez Doctor then proceeds to make good noises with a competent replacement show runner who never worked on Broadchurch in any capacity, just to make sure. Old monsters appear and stuff like that, and a fit bird enters the Tardis to the delight of all men over 40. But Gomez is having none of it, and maintains a monastic distance.
With order restored, and helped by an amazing central performance backed by intelligent, witty writing the BBC shunts the show all over the place until the ratings dwindle.