Rather coincidentally, I've been watching/listening/reading a lot of DW material that's included vampires, either the Great Vampires of old, their modern offspring - as in Jago & Litefoot - or the "man-made" vampires of the Forge. It got me to thinking... given the enmity between the Time Lords and the vampires, is there any circumstance in which the Doctor could take on a vampire as a companion? Following some form of the reluctant vampire trope? If so, which Doctor would make the most sense?
No, because the character would suck. Spoiler I shall now promptly go hide behind a sofa... Okay, in seriousness, why not? Continuity in the show hasn't always been consistent... and if written genuinely well, even those who would remember such continuity would be won over. Besides, a time war with Cybermen might change causal nature to the point the Dalek time war never existed or the Great Vampire war either. Dunno.
I'm also in the "why not?" camp. I can envision situations in which the Doctor would take a Dalek as a companion. He's had a Cyberman companion, Kroton, in the comics. He's even had the Master as a companion. So, enmity between Time Lords and vampires isn't an insurmountable issue, and the Doctor's going to do what the Doctor's going to do anyway. As I think about it, I can see some intriguing angles to explore -- what are the "rules of vampirism" for the character, what kind of blood does the character need and how does the character get it, how does the character function on the TARDIS team within the limitations of the "rules." At the same time, I think there would be a temptation to explore the true nature of the Time Lords/Vampires relationship with a vampire companion, that the conflict wasn't exactly what it was made out to be (which I seem to recall was a facet of Lawrence Miles' Interference), but I don't think that's really necessary and would probably overwhelm the storytelling. No, leave it with who is the vampire character, why does the Doctor take a shine to the vampire character, and what are adventures in the TARDIS with this vampire character like?
No, if only because I'm so sick of vampires in general, even if Doctor Who vampires are different enough from human vampires. That said, I agree that the notion of seeing The Doctor traveling with a member of a race that he's a sworn enemy of would be intriguing to watch. I've been a long-time fan of the idea of The Master traveling with The Doctor (which we got briefly in Scream of the Shalka) and I still wish Davies had taken that route in "The Last of the Time Lords" instead of just "killing" him off.
There's a Big Finish story where Nyssa is a vampire for much of it, though the Doctor manages to cure her at the end.
It was actually the first Virgin Missing Adventure novel in 1994, Goth Opera. She only survives because she (just barely) didn't feed on human blood before the being that turned her was killed. She tried to create a blood substitute for her to survive on in the meantime, but was unsuccessful. (That was also the 'episode' where Romana returned to Gallifrey from E-Space, and we see the beginnings of her rise up the political ranks.)
They could at least take a stab at it, but you would need a actor with goog acting teeth, and one that has no stake in the shows suckccess....... ...no...... I'l get me coat.