(Out of curiosity I google imaged combinations of DW actors alongside 007 actors; I found Tom and Pierce when the former guested in Remington Steele,
That fanzine I mentioned had a story with a Fourth Doctor/Remington Steele crossover.
Well, since Douglas Adams wrote for and was the script editor for Dr. Who, a 'Hitchhikers Guide to the Galaxy' and Fourth Doctor crossover seems pretty obvious.
Of course, but Peter Davidson was already in the Hitchhiker's Guide TV series. Mind you, he didn't play the Doctor.
I find crossovers incredibly problematic. 99.9% simply wouldn't fit with a different franchise.
The only things I could half way see working with Who is Hitch Hikers Guide, and at a real push, Bill and Ted.
The beauty of crossovers is that they don't need to fit flawlessly. They should fit plausibly to some extent, but keep in mind that our regular normal world doesn't have things like TARDISes that are bigger on the inside.
The franchises in that fanzine I mentioned included M*A*S*H (Fourth Doctor and Leela), Wizards & Warriors (short fantasy series from the early '80s), All Creatures Great and Small, Remington Steele, Star Trek, and quite a few others.
Here's the link to the Traveling Companion fanzines; I'm talking about:
https://fanlore.org/wiki/Travelling_Companion
The contents include:
Travelling Companion 3 is undated (likely 1984). It contains 158 pages and crossovers with
WKRP in Cincinnati,
The Phoenix,
Hill Street Blues,
Star Trek: TOS and more. The front cover is by
Gennie Summers.
- ads, editorial (2)
- cartoon by Michael Krause (3)
- Pivot Point by Marguerite Krause, art by Gennie Summers (Fourth Doctor crossed with Star Trek) (4)
- Limerick by Rebecca Ann Brothers (19)
- Wrong Turn at Albuqurque (sic) by Cheryl Duval (Second Doctor on Tatooine) (20)
- Cartoon by Summers and Sizemore (23)
- Seen and Unseen by Jody Lynn Nye (Susan and Narnia) (24)
- David's Song by Marguerite Krause (25)
- cartoons by Anne Davenport
- filks by Linda Terrell (28)
- Song Unsung by Linda Terrell, art by Cheryl Duval (Third Doctor) (28)
- A Time Lord by Cyndi Bayless, art by Caro Hedge (31)
- Hitchiker's Guide to the Daleks by Rebecca Ann Brothers (32)
- filk by Judy Nathanson, art by Hedge (34)
- Pair O'Docs by Marguerite Krause, art by Jane Fancher (Fourth Doctor crossed with WKRP in Cincinnati) (35)
- Advertisements (52)
- Whose Prime Directive by Cheryl Petterson and Susan Sizemore, art by Laurie Farkas (Fourth Doctor and Star Trek) (53)
- The Time of The Phenonix (sic) by Teresa Sarick, art by Phred (Fourth Doctor and the Phoenix) (61)
- Nor Isolde Either by Phillip Allen (Fifth Doctor and All Creatures Great and Small) (69)
- Impressions, Another View by Marguerite Krause and Susan Sizemore (73)
- Traveller's Return by Leah McGrew, art by Gennie Summers (Fourth Doctor and Time Tunnel) (74)
- And Magic is Loose in the World by Teresa Sarick, art by Rick Braunshausen (Fourth Doctor and Wizards and Warriors) (83)
- Steele Alive, Old Friend by Susan Sizemore (Sarah Jane Smith, the Brigadier, and Remington Steele) (106)
- Hold to Destruction by Linda Terrell, art by Rick Braunshausen (Fourth Doctor and BOLO) (120)
- Alight by Teresa Sarick, art by Caro Hedge (128)
- Is There a Doctor in the House by Leah McGrew, art by McGrew (Fourth Doctor crossed with M*A*S*H) (129)
- Advertisement (133)
- TARDIS on the the Hill by Sue Ann Sarick (sic), art by Laurie Farkas (Fourth Doctor and Hill Street Blues) (134)
- Broken Infinity by Karin L. Zygowicz, art by Caro Hedge (151)
- Private Place by Marguerite Krause, art by Gennie Summers (Fifth Doctor and Star Trek) (152)
- cartoon by Summers (157)
- filk by Jody Lynn Nye (158)
- back cover by Cheryl Whitfield Duval (160)
- art by Phred, Duval, Farkas, Davenport, Fancher, Summers
I'd forgotten about some of these stories, but then I never watched WKRP or Hill Street Blues.
Some of these fanfic authors went on to have professional writing careers.
I agree. With mundane series, it's easy enough to do a crossover -- it's not that implausible that, say, Jessica Fletcher and Thomas Magnum could live in the same reality, or that the casts of Law & Order and JAG might meet each other on a case. But with science fiction, the universe itself tends to have different physical laws, history, etc. in each series, so there are few cases where two series can logically be reconciled. And the alternate-history dodge doesn't make sense in cases where fundamental things like physical laws and the existence of entire planets and species are incompatible.
There's a fanfic story that crosses Murder, She Wrote with Keeping Up Appearances. Jessica Fletcher has to figured out who murdered Hyacinth. Since Hyacinth is such an annoying character, it could be any of over a dozen regular and recurring characters.
One of the more interesting crossovers I've ever read is Stargate/I, Claudius.
I apologize in advance...
Bill and Ted enter the TARDIS
Bill and Ted: "Whoa!"
Bill: "Ted my friend, this is a most bodacious display of transdimensional mechanics."
Ted: "Agreed, Bill my friend. Most resplendent."
Ted turns towards the Doctor.
Ted: "Dude! It's totally bigger on the inside!"
Bill: "How come ours doesn't do that?"
Doctor: "Because it was built by humans. Now, shut up and let me think.
Bill: "Absolutely, grumpy time traveler dude."
Ted: "Dude, check out this guy's guitar!
Bill: "Dude! You play? Do you want to join our band?"
Bill and Ted: "Wyld Stallions!" *air guitar*
*Doctor facepalms*
Yeah, I'll just show myself out...
This would be fun!
Actually, if you want to base a crossover on which actors have appeared together, then of course Doctor Who could be crossed with some of Kenneth Branagh's Shakespeare movies. After all, Derek Jacobi and Brian Blessed were in Henry V (not all Whovian stories actually need the Doctor), and Brian Blessed and Richard Briers were in Much Ado About Nothing. Oh, and Keanu Reeves was in that one as well. Of course he played the villain, but there's a way to get around that. It couldn't be worse than some of the drivel in the actual nuWho series that drove me to quit watching.
And a natural crossover would be Doctor Who/Harry Potter, with not one, but two Doctors' actors in that.
Though I'd really prefer a crossover with Harry Potter and BBC Merlin. I can imagine Kilgharrah the Great Dragon not dying after all, and instead transforming into an elderly wandmaker plying his trade in Diagon Alley.