lentää (to fly)Examples with other morphemes than -to can be found, but I can't be bothered to introspect for them all that much at the moment. In addition, there's two words that have exceptional singular partitives after a neutral root - usually, roots that only have neutral vowels trigger front harmony. I'll arrange the case forms here according to their morphological relation - i.e. the singular locative cases are indented from the genitive, because their formation can be predicted from the genitive, and the plurals from the plural partitive. A dash separates the case marker in the genitive and plural partitive from the singular and plural oblique stems.
lento (a flight)
viiltää (to incise)
viilto (an incision)
meri (sea, ocean)
meressä, merestä, mereen, merellä, mereltä, merelle
mereksi, merenä, merettä, meret (plural nom/acc!)
merta* I don't even recall the exact formation rule for merten/merien, but iirc it too derives from meri-. I get it right in speech, but don't ask me to tell you how it works. Oh, and both merten and merien are accepted forms - either due to standard Finnish taking both eastern and western forms, or due to both having coexisted widely.
merissä, meristä, meriin, merillä, meriltä, merille, meriksi, merinä, merittä, merine-(plus poss. suffix), merin,
One other word has the same exact behavior, viz. veri, blood. As a not fully native speaker but almost, my opinion on this particular pair of words might not be shared by everyone, but to me mertä sounds less wrong than vertä does - I am not sure whether if someone said vertä in a sentence, I'd even realize immediately what word was being mangled, but I think I would so with mertä.
Now, to the conlanging idea!
Let's have a couple (or more) of 'metaphonemes', " and ¤. " switches harmony to front harmony, ¤ switches to back harmony. Any other type of harmony could of course be useful, but front-back harmony with umlaut signs makes for a visually simple example. One could of course imagine that the best way for this to work would simply be a regular, realized phoneme that deviates from the expected harmony, and forces future suffixes to switch, as in the made up example below, where ko is part of the root:
pöläko, pöläkopa, pöläkora ...My thoughts here come very close to such a system, but what if, due to vowel reductions, this happens:
pöläko, pöläkopa, pöläkr ?The question mark serves to indicate my uncertainty here: should the lost /o/ still trigger -ra, or should the loss make the front harmony root trigger -rä?
This is where the " and ¤ would come in. They would be present in the root, never realized by themselves, but appear whenever a vowel is reduced out of existence. Thus, if the root were pöläk"o, we'd get pöläkrä, if it were pöläk¤o, we'd get pöläkra.
Thus, some form of vowel harmony exists in a language with such a system, but it's governed by some weird rules.