Something similar shows up in some of the Italian dialects. The relevant dialects are the ones with the following two features:
1) The Gorgia Toscana: After a vowel, p, t and k go to [ɸ], [θ] and [h]. This happens even when the triggering vowel is in the preceding word: la casa is [la'hasa] in dialects with this feature. But it only affects single p, t and k, not the geminate consonants pp, tt and kk.
2) Syntactic doubling: There are some specific words that, idiosyncratically, trigger gemination on the first consonant of the following word. This has the effect of blocking the preceding sound change. So a casa is [ak'kasa], and not [a'hasa].
If a Celticist were describing this sort of Italian they might say it had two mutation classes. Some words trigger "lenition" or "spirant mutation," others trigger "hard mutation."
If I understand correctly, there are even minimal pairs of words that only differ in which mutation they cause. So for instance, the clitic pronoun si doesn't trigger fortition, but the particle sì, meaning "if," does. This is a little like how, in Irish, a means "his" if it's followed by lenition, and "hers" if it isn't. The Italian examples are not as dramatic as the Irish ones, though — my perception is that there are a lot fewer minimal pairs like this in Italian.