How did Data's cat "Spot" change colors/breed/gender mid-series?

Possibility A- The cat died, got lost, whatever, and was simply replaced with another cat that Data with all of his creativity, decided to name Spot... again.

Possibility B- A significantly more unlikely possibility is that Spot and another cat strolled into a transporter beam that just happened to be having issues a la "Tuvix" style and the resulting combination of their DNA caused the change in the cat's appearance.

This is one of the examples of why production, ultimately, must trump plot in television and films. The original 'spot' probably couldn't be procured (for financial reasons or availability or some such) and so the producers just simply got any old orange stage cat to fill the place. Not to mention, that 'spot' was required to do various different types of stunts throughout the various episodes. Cats are notoriously difficult to train and so this would have required at least two different cats. Throughout the series, I remember reading somewhere, they ended up using something like 7 or 8 different cats.

Finally, due to constraints of the reality of producing a television show, an in universe explanation, in this instance, is just foolish.

He doesn't talk about it much^*, but Mot is quite the closet eccentric and very artistic. Although he is very discreet, and keeps them well covered, he has a number of very elaborate tattoos, is an avid reader of fashion e-zines, and a video blogger.

One of his "pet" projects (pun intended), is a video blog about hair dressing and fashion for pets. For this project, Data graciously allowed Mot the use of his cat, Spot.

This explains Spot's continued changes in appearance. It's really no different than the changes in appearance of Deanna Troi's uniform or hairstyle.

^*Meaning he doesn't talk about it at all; and I made up this entire answer

The (fully canon) Star Trek Encyclopedia has this to offer on the subject:

Spot first appeared in "Data's Day," but didn't actually get a name until "In Theory" (TNG). I "Data's Day," Spot was a male Somali cat, but in later appearances, Data's friend somehow became a female tabby. We speculate that Spot may be a shape-shifter or an unfortunate victim of a transport malfunction.

Out of universe, the change was due to the production team using a different animal suppliers.

Per Memory Alpha

Spot was played by unknown long-haired Somali cats in his first two appearances and trained by Gary Gero and Scott Hart from Birds & Animals Unlimited. Spot's appearance was changed into an orange tabby cat beginning with the sixth season when Rob Bloch from Critters of the Cinema took over the animal casting and training. During his time on The Next Generation, Spot was then played by Monster, Brandy and Bud and later also by Tyler, trained by Rob Bloch and Karen Thomas-Kolakowski.

When it was decided that Spot would appear in the first TNG feature film, Star Trek Generations, Critters of the Cinema trainers Bloch, Thomas-Kolakowski and Kelli Cole trained the cats Monster and Brandy and their back-ups Spencer and Zoe. While Monster appeared in the scenes earlier in the film, when a more spunky Spot was required, Brandy was the cat seen at the end of the movie. Critters of the Cinema was not called back for the production of Star Trek Nemesis.