Adaptive Conjoined Twins:
My answer is actually going to be a variant of my answer to THIS question based on some creative developmental handwavium. I would imagine a fantasy world where a developmental mutation occurs, is somehow taken up by a common virus, and spread to many new species. In this case, you need a stable genetic shift that causes essentially all fetuses to create conjoined twins. Fortunately, we're talking domesticated animals, so the evolutionary pressures have a lot more to do with what humans like, rather than what is adaptive.
You start with a dog that consistently creates conjoined twins that re-merge due to developmental genetic variants. Maybe this is because the dog is a fun chimaera with two heads and neat growth patterns. Maybe they think guard dogs with extra heads are terrifying (this is especially true if there are superstitions about multi-head dogs). Who knows? All the variants that are non-viable die, and the ones that are merely dysfunctional are kept as really cool pets. But they could be at least partly functional, as humans with two heads and conjoined twin syndrome are sometimes reasonably functioning. So for argument, one head is consistently functioning, the other not so much. The more functionality, the more people love them and select for them.
Now that you are selecting for crazy heads, A second mutation occurs. The non-functioning twin is getting different developmental signals (which is why it's the non-functioning one) and this one starts consistently growing two heads in a polycephalic manner. Now the resulting conjoined twin suddenly has THREE heads. This creates a huge stir among the breeders, who select for this like crazy. It LOOKS like a Cerberus, which may have been the original reason for the two-head breeding craze.
You could end right there, if you wanted. But with a selective pressure to have more function, eventually the two "minor" heads become able to move and articulate. Now your three-headed guard dog might actually have some real usefulness, and the lesser versions are phased out. Because this is all developmental, you'll probably still get a natural failure rate where variants regularly occur. As long as people like the three-headed dog, they will keep selecting for increasingly stable versions.
Any other Cerberus-like characteristics would be largely cosmetic and easy to select for.