According to what I remember from reading Japanese mythology and speaking with a Shinto priest, multi-tailed animals start off as just that, animals. As they age, one hundred years per tail, they eventually undergo a transformation where they literally grow another tail. This transformation also increases intellect and wisdom and size, as well as other characteristics.
The Nine-Tailed Fox is the pinnacle the development tree assigned to the lesser spiritual beings. There are also other animals which develop multiple tails, such as wolves and cats, among others. If they manage to survive 1,000 years they undergo yet another transformation into a "celestial fox" and become a greater spiritual being, apart and separate.
Note that a Japanese "fox" is actually a Tanuki. Thus fox mythology actually came from China to Japan around the 7th century, and was later incorporated into Japanese lore. Originally a malevolent and evil entity, stories and legends of the tanuki and fox became mixed and changed over time. Like the fox, the tanuki is also a trickster shapechanging being, thus this was an easy cross-over. In Japan, the fox was eventually linked with Inari, the rice-god as messengers.
In any case, as the science-based tag is being used, it is theoretically possible that such a fox could have a genetic structure that allows the creature to hibernate every so often and during said hibernation, sprout and grow another tail. It would be likely that there would be bone spurs or nubs present towards the end of the spine which will become the site of new tail growth, somewhat akin to antlers. Again like antlers, the fox could lose the tail and regrow it on a cyclic basis, with increasing numbers of tails being tied to age.