There are at least some cases in which this can be done, with different shades of meaning.
graecisso (-izo), āre, v. n., = Γραικίζω, to imitate the Greeks, to adopt a Grecian manner or tone: atque adeo hoc argumentum graecissat; tamen Non atticissat; verum sicelissat, Plaut. Men. prol. 7; v. Ritschl ad h. l.: graecizat, Consent. 1063 P.
atticisso, āre, v. n., = ἀττικίζω, to imitate the Athenian manner of speaking: hoc argumentum graecissat, tamen non atticissat, verum sicilicissitat, Plaut. Men. prol. 12; App. Flor. n. 18, p. 362, 12.
sicilisso or sicelisso, āre, v. n. Siculi, to imitate Sicilian manners: hoc argumentum graecissat: tamen Non atticissat, verum sicelissat, Plaut. Men. prol. 8; v. Ritschl ad h. l.
And then there are some in -or:
cornīcor, āri, v. dep. cornix, to caw like a crow (very rare): quid grave secum inepte, Pers. 5, 12; cf. Prisc. p. 828 P.; Hier. Ep. 125, n. 16.
rhētorico, āvi, 1 (ante-class.), and rhētoricor, āri, v. dep. (post-class.) [rhetoricus], to speak rhetorically or like an orator, Novat. ap. Non. 476, 6 (Com. Rel. p. 216 Rib.); act. form, Tert. Res. Carn. 5.
(Though I'll note that there's also rhētorisso, āre,.)
My understanding is that this tendency is more common in ancient Greek than in Latin, but that's just from something my first Greek teacher said ten thousand years ago, so it could be totally wrong.
In any case, it seems to be fairly rare; then again, it's fairly rare in English too—we might talk about somebody "Clinton-izing" something or "Coulter-izing" something (sorry, politics on the brain), but not very often.
EDIT: An explanation from a different angle from 1841's Linguæ Grammaticæ Rudimenta:
