I’ve often seen the Finnic languages considered to demonstrate that vowel harmony acts a counterforce to the common tendency for second-syllable (“stem”) vowels to trigger various conditional developments (umlauts) of first-syllable (“root”) vowels. At least within the larger Uralic comparative context, this indeed appears to be the case. There is even the illustrative case of Livonian, a Finnic language which has both lost vowel harmony and innovated a process of *i-umlaut (appearing e.g. in the nominative singular forms of nouns: *käci > ke’ž ‘hand’, *tammi > täm ‘oak’, etc.)
This however does not need to imply that vowel harmony languages are somehow categorically immune to umlaut developments. I’ve already briefly examined a possible shift *ë-o > o-o for Votic. It also seems another somewhat similar case can be found as well, this time though appearing wider across Finnic. More interestingly, this involves umlaut “against the grain” of Finnic vowel harmony — in backness.
To start from the beginning, today’s observation traces its roots to Janne Saarikivi’s paper “ystävästä, uskosta ja vokaaleista“, published 2010 in the eminent Finnish etymologist Kaisa Häkkinen’s Festschrift Sanoista kirjakieliin (SUST 259). This treats the Finnic word group for ‘friend’, whose representatives include Finnish ystävä, Estonian ustav, Livonian ustõb (and which has also been borrowed to Samic; e.g. Northern Sami ustit). The words clearly resemble fossilized participles, but various competing ideas have been suggested on what the original root would be, exactly. Saarikivi argues convincingly that the best option appears to be connecting the words to the same root as e.g. Fi. usko(-) ‘belief, to believe’: i.e. *uskV-(t)ta- > *usta- ‘to be true/reliable, to consider a friend’ > *usta-ba ‘(one who is considered a) friend’.
His explanation for the phonetic development is, however, slightly awkward. Drawing in some known parallels from Permic and Khanty, and bringing in some new Samic evidence, he suggests that this word group could be traced back to a Proto-Uralic (transitive) verb root *iskə- ‘to believe in’. From this a reflexive (intransitive) derivative *iskə-w > *isk-o- would have been created, which would have been backed to *usko- in Proto-Finnic; followed by re-fronting in Finnish, for “similar unclear reasons” (a very hazardous form of argument IMO) as appears in some other words, e.g. Fi. muhku ~ myhky ‘clump’.
Petri Kallio has instead proposed in passing what seems to me like a clearer explanation; again in his paper “Jälkitavujen diftongit kantasuomessa” that I seem to have brought up a couple of times by now.  According to him (and I agree), a more expected initial development in Finnic would be *iskə-w- > *iskü- > *üskü-. The labiality assimilation here is a known sound development — and incidentally presents another minor example of umlaut in Finnic. Following this he suggests resuffixation: *üsk-o(-) > usko(-). This latter step involves what seems like a previously unproposed sound development: *ü > u by the influence of second-syllable *o.
Phonologically, this sounds reasonable: it’s generally accepted that *o in unstressed syllables remained outside vowel harmony in Proto-Finnic, and o/ö-harmony as found in modern Finnish/Ingrian/Karelian (and partly Veps) only emerged later. In other words, PF second-syllable *o was indeed specified as [+back], and could pass this feature also to a first-syllable vowel.
(Also, though Kallio does not say as much, this two-tier scenario seems to even explain Fi. ystävä. Back when *UstA- was still around as a separate verb ‘to consider reliable/a friend’, we could consider *üskü-(t)tä- > *üstä- the regular development, attested in Finnish; competing with a variant *usta-, attested in southern Finnic and Samic, which would have gained its /u/ by analogy with *usko(-).)
Getting to the point though, this idea has drawn my attention to what looks like a phonotactic gap in Proto-Finnic. Although we can reconstruct PF *-o following most first-syllable vowels (e.g. *ilo ‘joy’, *veto ‘pulling’, *käko ‘cuckoo’, *pato ‘dam’, *pëlto ‘field’, *kolo ‘hole’, *puno- ‘to weave’ ), there do not seem to be any recognized cases of the vowel structure *ü-o. Even in modern Finnish, cases of y-ö are fairly rare. This seems like grounds to formulate a hypothesis. I suggest that Kallio’s proposed “o-umlaut” development is not merely an isolated sporadic example, but a full-fledged soundlaw: Proto-Finnic *ü-o has regularly yielded later u-o.
Investigating this possibility is going to be a bit difficult, though. PF *-o continues to have no firmly established regular origin (other than the dissimilation *ai > *oi in unstressed syllables after *a, *e, *i, which is not relevant here), and is mainly concentrated in derivatives and loanwords. Some particular morphological groups’ cognates in Mordvinic suggest the development *Aw > *o, but in others there seems to be no indication of this.
Regardless, here are a couple of doublets & such I’ve identified in Finnish that might be indicative of this same “o-umlaut” as usko(-):
- ulotta- ~ ylettä- ‘to reach smth’. The former’s been considered to derive from the postposition root ulko- ‘out’, the latter from ylä- ‘up’. While these are fairly close-by concepts, and while there are even particular expressions that appear to support this derivation (e.g. ulottaa kätensä ‘to extend / reach out a hand’, ylettää kattoon ‘to reach (up ’til) the ceiling’), these could regardless be due to semantic contamination. This seems to be confirmed by Veps /uluta-/, Livonian ulātõ, which both suggest roughly PF *ulotta-, not *ulgotta-. Alas, the 2nd-syllable vowels in these are aberrant, which suggests that the history here has probably been somewhat more complex.
SSA proposes an alternate analysis: deriving ulotta- and ulko- both from a root *ula-, allegedly also present in ulappa ‘open sea’ and ullakko ‘attic’, but this seems to run contrary to all regular patterns of Finnic word derivation. 
- luppo ‘beard lichen’. No Finnic variants pointing to *ü are known, but the word’s Samic cognates interestingly enough uniformly indicate an original front vowel. Although there are various known cases of *ë/*o vacillation in Samic, both PS *lëppō and the Finnish form could also simply derive from earlier *lüppo.
A possible problem though is that the Finnic word is only found in Finnish and northern Karelian, and perhaps is rather to be explained as a Samic loan. It would be possible to speculate with late retention of *ü in early Samic, or an umlaut development of *ë-ō in the loaning Samic variety, but I’ve nothing solid to go on on with that line of thought.
- pursto ~ pyrstö ‘tail’. This is one of the examples of “frontness alternation” that Saarikivi mentions. Supposing *pürsto as a starting point would allow some Finnic dialects to evolve pursto, others pyrstö. On the other hand, it might be a problem that the words likely derive from Germanic *burstō- ‘bristle’ (which may seem semantically distant, but Karelian and some Finnish dialects retain an intermediate sense ‘dorsal fin’).  SSA suggests that pyrstö, the variant with a narrower distribution, could be due to contamination with pyrise- ‘to shake’ (intr.), pyristä- ‘to shake’ (tr.), which seems equally possible.
- ruho ‘body’ ~ ryhä ‘hump’. A comparison that would not have struck me as obvious, but SSA analyzes the latter as a “variant” of the former. Normally we’d expect an A-stem to be more original than an o-stem though. This is also suggested by the loan etymology of the words from Germanic *xruza- ‘corpse, pile’. Or, given the y-vocalism, perhaps rather from Old Norse *hryRa-? Thus *rühä → *rüh-o > ruho seems like a possibility.
- runno- ‘to cram, mangle’ ~ ryntää- ‘to rush (into)’. The interference of various other words is possible (e.g. ruhjo- ‘to injure, mangle’, säntää- ‘to rush’) but what makes me suspect indeed common origin is the irregular variation nn ~ nt, appearing in both groups here. In standard Finnish the two verbs themselves have ended up in different “grades” (not quite in accordance with regular consonant gradation), but further derivatives include e.g. runtu ‘dent’, rynniä ‘to rush suddendly’ (punctual).
- rusto ‘cartilage’ ~ rysty ‘knuckles’. SSA connects the two as being of “similar descriptive origin”, but they could be connected as straightforward parallel derivatives (*rüst-o, *rüst-ü). Less clear is if rusikka ‘fist’, also mentioned by SSA, is a part of the same cluster. This does not seem necessary, but if it does, *u will probably have to be more original (and we’re back to square one).
None of the cases appear crystal clear, but being able to get six examples together still suggests to me that this is probably on to something. OTOH also chronology seems slightly problematic here. The Saarikivi–Kallio scenario for usko would require that *ü-o > u-o was later than the assimilation *i-ü > *ü-ü; yet this has also been quite late, being e.g. found in (standard) Finnish (*pisü- > pysy- ‘to stay’, *pistü > pysty ‘erect’) but not in several dialects of Karelian (pisy-, pisty).  My proposed new derivation of ryhä~ruho from Proto-Norse rather than Proto-Germanic would also require a date well after Proto-Finnic for this change. But if it rather dates to the common (Western) Finnish era, then even counterexamples with narrower distribution in Finnic become relevant. Some troubling cases might be the following:
- kylvö ‘sowing’, kyntö ‘plowing’ (← kylvä- ‘to sow’, kyntä- ‘to plow’). These are a part of the wider pattern of deverbal -O/U-nouns. The pattern -tA- : -tO is particularly productive though (kääntö ‘turn(ing)’ ← kääntä- ‘to turn’, säätö ‘adjustment’ ← säätä- ‘to adjust’, ääntö ‘articulation’ ← ääntä- ‘to articulate’, etc.), which might have motivated the creation of kyntö in place of expected kunto, followed by semantic analogy to produce also kylvö? Dialectally, a variant kylvy is fairly widespread (and even kynty is attested).
- pyytö ‘plea’ (← pyytä- ‘to ask’). A similar derivative as the above two, but here we could additionally suppose that long yy was perhaps unaffected by this umlaut.
- kytö ‘slash-and-burnt field’. Likely also a derivative of the above type, from kyte- ‘to smoulder’. However, from an e-stem verb I’d expect kyty, which is indeed attested in a few dialects (cf. also e.g. kylpy ‘bath’ ← kylpe- ‘to bathe’, käsky ‘order’ ← käske- ‘to order’, sylky ‘spittle’ ← sylke- ‘to spit). Could kytö be a late re-suffixation to avoid homophony with kyty ‘brother-in-law’?
- tyttö ‘girl’; fairly widespread, with cognates found in most of Northern Finnic, as well as in Votic. However, the variant tytti seems to be older yet, with cognates extending also to Estonian and Livonian. This seems like a similar innovation as the replacement of Fi. isä ‘father’ with iso in Karelian.
It appears that a clearer picture of the development of 2nd-syllable labial vowel suffixes in Finnic will be needed for making progress here.
 Footnote 13, to be specific. For the further ref details, see e.g. my previous post. Perhaps I should establish a policy to add anything I cite at least twice to my Literature page?
 The idea of a contrast between *e-o and *ë-o (cf. Estonian vedu vs. põld : põldu-) is provisional and not particularly crucial to the point.
 I wonder rather what’s exactly the relationship between ullakko and lakka ‘roof’. SSA suggests irregular contraction from *ula-lakka, but perhaps there is rather some kind of a prefix *ul- in here. In that case, it would be also possible to analyze ulappa as *ul-appa, where the 2nd component would probably derive in some fashion from Proto-Norse *haba- ‘sea’ — probably thru Samic *āpē ‘open space’, in light of the developments *h > ∅ and *b > pp (similarly to what we see in northern Finnish aapa ‘open bog’). While very hypothetical, this approach still seems more promising to me than the notorious proposal that ulappa would be one of the no more than two or three Finnic words to have allegedly retained the Proto-Uralic derivational suffix *-ppa. — It would even be formally possible to derive ulotta- as *ul-otta-, i.e. based on the verb otta- ‘to take’?… probably not a good idea though.
 E.g. Wiktionary appears to have *bursti- though, which could allow deriving an i-umlauted reflex in Finnic after all; but this looks like a reconstruction mainly based on English. Hellquist’s old Svensk etymologisk ordbok suggests *burstiō-. I am not able to assess offhand which of these stem type variants is best supported.
 Or could these be late analogical reversals, on the basis of related formations such as *pistä- ‘to stick’?