Yes this is a real thing that was made into a comic. It mostly features the Eleventh Doctor, Amy, and Rory with the cast of the Next Generation.
How can they cross over when the show Doctor Who has clearly mention Star Trek to be a work of fiction in their universe? Well that's answered in the comic. They don't exist in the same universe. The Doctor Who characters crossed dimensions to get to the Star Trek universe.
The Doctor tells Amy and Rory that he didn't even know the word Klingon till after he saw Lt. Worf.
Later in the story the Doctor remembers meeting the original series Enterprise crew in his fourth incarnation but also remembers not remembering it.
When meeting Guinean in ten forward both she and the Doctor mention how they know each other in the past and yet at the same time they also realize this is the first time they've actually met each other. Both the Doctor and Guinean are sensitive to changes in history that shouldn't exist which is why they're the only ones aware of the fact that they don't belong in the same universe. Amy and Rory's memories were probably altered as well but they're likely not aware of it since neither one ever mentions Star Trek being a TV series in their universe.
Anyway, it's Doctor Who and Star Trek, if you know both franchises you've probably guessed by now who the villains are. The Borg and the Cybermen are very similar to each other and it's the Cybermen who initially make the trip into the Star Trek universe in order to make contact with the Borg.
In a flash back as the Doctor remembers the original series Enterprise crew the comic also depicts classic era Cybermen. No Borg because they were never in the original series. Though it would of been interesting if they tried to come up with a design for what a Borg might have looked like if they were created back in the 70's.
Anyway... there's also a odd reference to the 4th Doctor in a comic before the flash back even happens. When the Doctor first arrives on the Enterprise his TARDIS materializes inside the holodek while there's a program running. Initially they believe they're in San Francisco in the 1920's. There's a panel in the comic where you can see they're on 4th Street and there's a sign on a building that read's "Tom's Bakery"... so I wander if Colin's Bakery is on 6th Street? Anyway they figure out that they're not actually where they thought they were after they run into Data who the Doctor quickly realizes is an android.
Anyway... later on the Cybermen and Borg alliance breaks down as the Cybermen betray the Borg, beginning to upgrade them into Cybermen. A few Borg manage to escape, including one known as the Conduit. He contacts the Enterprise for help in defeating the Cybermen. Picard refuses because of the events of the TV episodes "The Best of Both Worlds" parts 1 and 2 where Picard was assimilated into the Borg collective and given the designation Locutus. That was also known in universe as the battle of Wolf 359 to which the Doctor mentions, "Bad Wolf again."
In case I forgot to mention it earlier, this story line goes on for eight issues.
Anyway as mentioned before Picard wants to just let the Borg and Cybermen destroy each other. However the Doctor takes him into the TARDIS and shows him what the future will be if he doesn't help the Borg. We get to see different alien races from both Doctor Who and Star Trek as Cybermen. Probably the only time we'll see that since normally they can only upgrade humans. The other reason they were able to upgrade other races is because of the technology they got from the Borg.
Picard reluctantly agrees to help but under specific circumstances. He has the Borg meet him off ship, and the Conduit has everything needed to assimilate them removed from his body before he's allowed on the Enterprise. As it turns out the Cyberman have basically deleted the network that links all the Borg to the collective. In order to restore that network they have to travel back in time to a time where they know the Borg will be so they can download a copy of that network to bring back with them to the future. It just so happens that the time period they have to go to is Wolf 359. The Doctor, Amy, and Rory go alone as that event is a fixed point and the Doctor feels the Enterprise crew shouldn't have to live threw it twice. Anyway this makes me want to watch those episodes again with the knowledge that the Doctor was there on the Borg cube going completely unnoticed as the Borg don't notice anyone that they don't perceive as a threat. They even met Locutus but he didn't notice them despite being right in front of his face.
They could easily actually make this a thing with current technology. Editing Matt Smith, Amy, and Rory into those episodes. Considering the Borg don't even need to react to their presence they just need to be there. But I'll settle for just imagining that they're there off camera, doing their thing to stop the Cybermen in the future and then leaving.
There's a kind of funny part where a Cyberman looks at Data and says "This unit doesn't seem to be in need of upgrading" do to the fact that he's already a machine.
The do finally manage to stop the Cybermen and restore the Borg collective. The Conduit betrays them once everything is done as it turns out everything needed to assimilate organics was removed but he still had the capability to assimilate technology and he attempts to assimilate the TARDIS. However the T.A.R.D.I.S. energy moves into Data and the Conduit fails.
Finally the Doctor, Amy, and Rory leave to return to their own universe but there's an extra panel showing the Borg making plans to master time travel. This essentially means that the movie First Contact, where the Borg travel back in time changing the entire history of the federation, it's the Doctor's fault that happened. This seriously makes me want to watch First Contact again knowing that their experience with the Doctor and the T.A.R.D.I.S. is what gave the Borg the idea to do that in the first place.
I don't know if these comics are really cannon with the series, either of them, but they seem to fit in so well. The writer seemed to take care to write it in a way that didn't create plot holes with the shows. There are even references to help you narrow down approximately where in the two shows histories that they're suppose to line up. We know that the Star Trek side of things is some time during or after the fourth season but before the movies. The comic also references Rory's time as a plastic Roman and A Christmas Carol so they must be some where in season 6 or 7. Obviously before the Angels Take Manhattan because Amy and Rory are still with him. That is a rather long window both ways where these events could of happened. There's no way to really pin point it any closer but it's at least narrowed down. And Amy would know what Star Trek is by this point in the comic since the reference to it in the show would of happened before this. The only real flaw is that the Doctor says once they leave they'll still remember those events. And because they travel in the T.A.R.D.I.S. I thought Amy and Rory were also to be aware of changes to the time line, which means it's very odd she never makes any reference to the fact they're in a T.V. show. I suppose you could explain it away by saying that just because she heard the title of the series once doesn't mean she's recognize the characters unless it was established that her character is a Trekie.
They should do a Mini-episode of Doctor Who where Amy and Rory discover Star Trek for the first time, just happen to be watching that episode, and then realize that they were there on that Borg cube.
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