I think the answer to this is probably many
After a short think, the first example I was able to find was:
Do Androids Dream of Electric Sheep?, by Philip K. Dick was adapted as
Blade Runner, directed by Ridley Scott, which in turn was adapted as
Blade Runner: A Story of the Future by Les Martin
Philip K. Dick approved of the movie despite the ...
Planet Of The Apes (1968) was based on French author Pierre Boulle's 1963 novel La Planète des Singes. After becoming a movie and additional sequels, it was further developed into cartoons, TV series and comic books.
Additionally, all of the original sequels spawned novelizations by established science fiction writers of the day, each of which went ...
If you consider a graphic novel to be a novel, then the graphic novel V for Vendetta (written by Alan Moore and illustrated by David Lloyd) was adapted as a film (directed by James McTeigue and written by the Wachowskis), which was in turn novelized by Steve Moore (no relation to Alan Moore).
The film had a number of differences from the graphic novel, and ...
Yennefer's backstory is aluded to in The Tower of Swallows:
Janka! Dear Janka!
Take this hunchbacked monstrosity from me! I don’t want to look at it!
She’s your daughter as much as she is mine.
Indeed? The children I have sired are normal.
How dare you… How dare you suggest…
It was in your elven family that there were witches....
In 1992 Francis Ford Coppola did his version of Dracula, released under the title "Bram Stoker's Dracula". Apparently the original novel was not adequate so a novelization was published (by James V. Hart and Fred Saberhagen).
Another example, years ago someone showed me a copy of H. Rider Haggard's "King Solomon's Mines" with a picture of ...
The bad endings reflect Bill's view on the world.
The endings are considered bad because they are sad. At some point in the movie (I can't find the script, or subtitles as of this date) Bill complains to the dislikers that his endings, although bad, are realistic.
Life isn't always a fairy tale, and things don't always end happily.
This reflects Bill's ...
As a biopic, it's accepted that the picture stays fairly close to the book's depiction of events. There is a slate.com breakdown that goes through several scenes and compares them between the book and the movie.
Where the accuracy is called into question is not in the book vs the movie, but in the book vs real life. The slate article notes a few of these, ...
One relatively clear-cut example is The Wicker Man, which "is a 1978 horror novel written by Robin Hardy and Anthony Shaffer. It was based on the 1973 cult horror film The Wicker Man, directed by Hardy and written by Shaffer. [..] The film itself is loosely based on the 1967 novel Ritual by the actor and novelist David Pinner."
If you'll expand ...
An early almost-example is the novel The Circular Staircase, which was adapted into the play The Bat, which was separately adapted into novel The Bat and movie The Bat.
As no-one seems to have mentioned them yet, James Bond, The Spy Who Loved Me and James Bond and Moonraker are novelisations of the relevant Bond films, which have no resemblance to the original novels by Ian Fleming whose titles they bear.
(well, the OP did say "regardless of how faithful the adaptation was")
Another example to the great ones given previously:
In 1937, Frederic Dannay and Manfred Lee (writing as Ellery Queen) released The Door Between.
In 1940, it was adapted as Ellery Queen, Master Detective, directed by Kurt Neumann and written by Eric Taylor.
Finally, in 1941 the novelization of the movie was published as Ellery Queen Master Detective (...
Another example: Snow White and the Huntsman.
Loosely based on the original fairy tale, which has been novelized many times (a.o. the brothers Grimm.)
The 2012 movie got is own novel, written by Lily Blake.