It's not inappropriate if you go at it from a fanfiction angle. Doctor Who is one of those franchises that can be crossed over with literally anything. There was a fanzine called Travelling Companion and one issue was purely crossovers. It was amazing how well the authors handled stories like the Fourth Doctor and Leela ending up in a situation when they drop into the 4077th in M*A*S*H or the Fifth Doctor goes for a stroll on one of the occasions when he, Nyssa, and Tegan spend a little time in 20th century Earth and he's mistaken for a vet named Tristan Farnon (from All Creatures Great and Small) - and promptly ordered to assist a farm animal that's having trouble giving birth (I don't remember if it was a cow or sheep).
There was one involving Remington Steele (detective show co-starring Pierce Brosnan), and of course there were a couple of Star Trek ones - one of them was not only a crossover with Star Trek in general, but also with the Valjiir Continuum (the series of fanfic stories linked in my sig).
I've got a few of my own Whovian crossovers planned - one in which the Fifth Doctor, Tegan, and Nyssa (haven't decided yet whether Turlough will be part of it) meet the Jeremy Irons/Francois Arnaud version of The Borgias, and a Tenth Doctor one that's a crossover with Downton Abbey (Dowager Countess Violet discovers, to her shock, that Isobel Crawley is really a 21st-century politician named Harriet Jones, who was stranded back in the 1800s and while making a life for herself, married into the Crawley family, had Matthew, and basically became Isobel Crawley). The Tenth Doctor finally realizes he should have gone back for her, and misses the right time by only a few decades or so. I don't remember what happened to Harriet Jones in the actual nuWho show, but I just thought it would be fun to try this, as the same actress played both roles. And who knows, maybe Violet might be up for a short time trip of her own.
The very first idea I ever had for a Whovian crossover, though, literally came in a dream. I was really into The Crow: Stairway to Heaven back in the late '90s, and one night I dreamed most of an episode that was a crossover with the Fourth Doctor. Of course I don't remember most of it now, but the basic idea hasn't been forgotten.
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