This word was used by Pliny the Elder in The Natural History, and the text contains a footnote that addresses your question well:
[Versipellis] literally means "changing the skin;" it was applied by
some ancient medical writers to a peculiar form of insanity, where the
patient conceives himself changed into a wolf, and named λυκανθρώπια,
"lycanthropy." The word appears to have been in common use among the
Romans, and to have been applied by them to any one who had undergone
a remarkable change in his character and habits; in this sense it is
used by Plautus, Amphitryon, Prol. 1. 123, and Bacchides, A. iv. sc.
4, 1. 12.—B.
In case you're unfamiliar with the story of Amphitryon, it involves Jupiter transforming into the likeness of Amphitryon in order to seduce the latter's wife. In the text of the play, Plautus wrote:
Nam meus pater intus nunc est, eccum, Juppiter:
vortit sese imaginem,
Omnesque eum esse censent servi, qui
Ita versipellem se facit, quando lubet.
In Bachides (Act IV, scene 4), Plautus wrote:
improbis cum improbus sit, harpaget, furibus
vorsipellem frugi convenit esse hominem,
sapit: bonus sit bonis, malus sit malis;
utcumque res sit, ita
Here's a translation for that:
He must be a rascal among rascals, rob robbers, steal what he can. A
chap that's worth anything, a chap with a fine intellect, has to be
able to change his skin. He must be good with the good and bad with
the bad; whatever the situation calls for, that he's got to be.