The Death Zone is active once more, and the Doctor is being time scooped once again.
Unfortunately, the time scoop is falling on inoppurtune moments. The Tenth Doctor is taken, but it is as he has been aged 900 years in The Last of the Time Lords. Eleven is taken in his final days in The Time of the Doctor. Fifteen is scooped immediately after being animated in Lux.
What else are some of the worst moments the Doctor could be plucked out of time for a multi-Doctor story?
The Third Doctor is taken as he’s showering in Spearhead from Space.
1 mid cocoa proposal to Cameca
5 as he’s dying of Spectrox toxaemia while carrying Peri to the TARDIS
Ooh fun idea!
10 scooped immediately after Rose is sucked into the void and scooped into Pete’s world. So he’s just really emotional and not in the mood. The Raston Warrior robot jumping all over the place trying to kill him, whilst 10 is just crying and going “it’s not fair”
12 scooped on his last day with River on Darillium, and is worried about getting back before the sun sets.
14 scooped just as the memories are coming back to Donna 
“It’s really important that I’m sent back there”
Or any companion’s first alien planet would be funny: imagine 11 taking Clara to Akhaten, then immediately being scooped away. The companion has to cope with an alien planet and being stranded there.
Going deeper for a moment – imagine if the First Doctor was plucked out of time for The Five Doctors from the moment he’s plucked out of time from The Three Doctors 
Suddenly the Second and Third Doctors see him vanish from the TARDIS scanner right as he’s about to explain the time bridge to them.
Plucking the Tenth Doctor out of time right as he’s racing through the Library to upload River Song from the sonic. Would the sonic’s battery drain out, thus losing the ability to save River, or would it remain in statis until he’s put back into place? 
2nd and 6th Doctors mid trials
Love the idea of Mindwarp ending like this:
Sixth Doctor: “I was taken out of time for another reason, and I have every intention of finding out what it is!”
And suddenly – pop! – he vanishes into thin air, as the Inquisitor and Valeyard look around, completely bewildered.
The First Doctor is taken from any of the following moments: the escape to the TARDIS in ‘An Unearthly Child’; his confrontation with Ian and Barbara in ‘The Edge of Destruction’; or his attempt at escape on Kembel as the Time Destructor activates at the end of ‘The Daleks’ Master Plan’.
The Second Doctor being taken away during the final fight in ‘The Enemy of the World’ would be horrible for Jamie and Victoria. Salamander would win! Alternatively, plucking the Doctor out from the Land of Fiction would be just as dire for his companions…
The Third Doctor coming fresh from ‘The Green Death’ would be interesting, if only to see how different he is with Jo’s departure so fresh to him.
The Fourth Doctor during Season 16 would be fascinating. Would he be worried that the Black Guardian might follow? Could the Black Guardian follow? If not, take him during the E-Space trilogy so Romana or Adric end up stranded for a little while, meanwhile we end up with a more dour Doctor from Season 18, haha
The Fifth Doctor… It’s tempting to say either immediately after ‘Earthshock’/just before ‘Time Flight’, or even during his journey back to Peri in ‘The Caves of Androzani’, but I think it would be funnier if it was after ‘The Five Doctors’—he’s just dealt with his past, and now he’s got to (potentially) deal with his future!
The Sixth Doctor during ‘The Twin Dilemma’ feels like the only right call. But, if post-regeneration stories are off limits, then I’ll choose the aftermath of ‘Mindwarp’ with that grief still fresh.
The Seventh Doctor would depend on if expanded material counted. I imagine it’d be a toss of the coin if he showed up from the Timewyrm arc, what with how not-all-there he was. I’ll settle for ‘Remembrance of the Daleks’, however, hopefully with the inclusion of some contemplations from the Doctor about the consequences of his actions…
The Eighth Doctor would need expanded material to count, but there’s far too much for me to choose from. I’ll choose ‘Terror Firma’; have the Doctor terrified that he’s abandoned Charley and C’rizz just like he did Samson and Gemma…
The War Doctor goes without saying. I feel like any day would be the worst for him, and we’ve already seen him on the Last Day…
The Ninth Doctor right after his argument with Rose in ‘Father’s Day’. I feel like he’d be a uniquely prickly type in that context.
The Tenth Doctor during his Time Lord Victorious moment in ‘The Waters of Mars’. I imagine he’d try everything he could to escape and get back to Bowie Base One. But, if he didn’t, I’m sure he’d be terrible company for the other Doctors…
The Eleventh Doctor just before going into self-imposed exile after losing Amy and Rory. Again, the grief—I feel like there’s a pattern here…
The Twelfth Doctor during ‘Hell Bent’. I don’t think that warrants explanation.
The Thirteenth Doctor is one I still can’t comment on, but I’m going to hazard a guess and say that she might not be ideal to be around if she’s taken from the moment she learns about the Timeless Child…
The Fugitive Doctor is a tricky one. Let’s just say at any point; I feel like most other incarnations would have a very difficult time with her, not that she’d care, haha
The Fourteenth Doctor between ‘Wild Blue Yonder’ and ‘The Giggle’, ideally before the TARDIS lands and he sees Wilf.
The Fifteenth Doctor during ‘The Interstellar Song Contest’. That wouldn’t be pretty…
Damn, I was too slow… 
I think six was also time scooped out of his trial in The Eight Doctors!
Poor fella is like a yo yo. Spends more time being scooped out of the trial than in the trial!
Time Crash – suddenly, the TARDIS crashes into itself. The Fifth Doctor appears in the Tenth Doctor’s console room. Just as they start bickering, the Tenth Doctor is plucked out of time, leaving the Fifth Doctor stranded.
10 during or right after fires of pompeii and then running into 12 and being bewildered.
For some reason 4 doesn’t get scooped again and neither does 10. So there’s the curator and 14 but everyone keeps thinking it’s 4 and 10 just older
The Tenth Doctor is taken out of time immediately after his regeneration from the Ninth, so he’s asleep in the Tyler’s flat. He won’t wake up no matter what, so the other Doctors have to just carry him over their shoulder for the entire adventure. Only once he’s returned to bed in his timestream does he wake up, confused, for a second, and then falls back asleep.
10 being scooped out of “Time Crash”. Yes, scooped from a multi-Doctor story for another multi-Doctor story, oh boy I’m evil incarnate >:)
This way the Doctor won’t be able to pluck the Belgium-sized hole in the universe, since 10 did it, while observing it through 5’s eyes. And now 5 has nothing to observe and remember, and thus boom - the fabric of reality now has a Belgium-sized hole in it :DDDD
Last few i have
A glitch happens and 1 (Hartnell) 1 (hurndall) and 1 (bradley) are all taken
same with 6 (baker) and 6 (mccoy with baker wig)
All the 8th doctors shalka, fatal death, TV movie
OMG the most obvious answer for 1 
during Planet of Giants
What would happen if the Thirteenth Doctor was plucked out of time mid-forced-regeneration? I like to imagine she’d end up wherever, ‘glitching’ between Jodie’s Doctor and Sacha’s Master.
The Third Doctor while very slowly and agonisingly dying of radiation poisoning would be rough, considering the one short story set in that time describes him as essentially catatonic iirc.
Take Eight at any of the occasions where they’ve just lost their memory and that’d be awful.
EDIT: changed “shirt story” to “short story”, though now I want a Third Doctor shirt story…
I‘ll wear it over my TLV t-shirt and Tom Baker boxer shorts!
Just considered, the Sixth Doctor from Jubilee would be a rough choice…