The Finnish verb seistä ‘to stand’ has an interesting defective inflection. Only forms with the consonant stem seis- exist, including e.g. the citation form; some other infinite forms (e.g. seisty ‘having stood’, seisten ‘by standing’), and several imperative forms (seiskäämme ‘let us stand’, seiskööt ‘let them stand’). This includes also an archaic 2nd person imperative seis!, but now only fossilized as the interjection ‘stop!’.
For any other forms or derivatives, the stem of the synonymous seisoa is used instead (seison ‘I stand’, seisoo ‘s/he stands’, seisova ‘standing’, seisottaa ‘to make stand’, seisokki ‘stoppage’…) This is also an entirely regular verb in its own right, allowing just fine the same forms that were built from the stem seis- (seisottu, seisoen, seisokaamme, seisokoot…), though my impression is that these remain rarer in use. Hence this is not quite a classical case of suppletion, as much as one verb “leeching” on another.
A similar situation is found widely across Finnic: e.g. Estonian seisma : seisan (showing full suppletion), Votic sõissa : sõisaa, Võro saisma : saisa. (The variation ei ~ õi ~ ai is a regular correspondence, normally analyzed as deriving from *ai, though it remains under some debate what the conditions of this change have been.) We can most likely trace this stem type variation already to Proto-Finnic, and reconstruct *sais- ~ *saisa-. From the Votic village of Itšäpäivä, a form sõisõa has been recorded, and this could in principle retain the former’s expected vowel stem *saisë-, but given the extremely limited distribution, it seems more likely to me that this is either a backformation, or perhaps a secondary illabialization from *saiso-.
The forms pointing to *saiso- are most likely best analyzed as derivatives of *saisa-, as indicated by e.g. Estonian seisuma ‘to leave to settle’. The reasons for this replacing the basic root *saisa- almost completely across Northern Finnic (only some derivatives remain, e.g. the Fi. adverb seisaallaan ‘standing’) remain obscure to me.
It appears to me that the variation between *sais- and *saisa- can be clarified though. Looking wider across Uralic, a seemingly different alternation between front and back variants appears in the cognates: forms like Samic *ćōńćō- (with palatality assimilation: *s-ś > *ś-ś) and Mansi *toońć- indicate PU *sańśa, while forms like Mari *šĭńće-, Samoyedic *tänsä- indicate PU *säńśä-. Yet this can be seamlessly connected to the alternation in Finnic. As a rapidly increasing [1] amount of evidence shows, *ä-ä regularly yields precisely pre-Finnic *a-ə > Proto-Finnic *a-ë, and hence the front variant *säńśä- will make the best available source of the consonant-stem variant *sais-.
Presumably, shortly after this change, the variants *saisa- ~ *saisë- were found to be too close to one another, and eventually merged in favor of a single productive stem *saisa-. Yet this probably happened only after the creation of various consonant-stem inflected forms from the latter, which would have been able to survive thanks to being at least marginally lexicalized. If some degree of suppletion resulted initially, and forms like Fi. seisottu were later recreated anologically, is probably impossible to tell as long as Proto-Finnic remains unattested.
These Finnic consonant-stem variants of ‘to stand’ also seem to provide the first direct line of evidence that both variants existed side by side already in Proto-Uralic (*sańśa- ~ *säńśä-), rather than the latter resulting from “sporadic” or “affective” palatalization in various descendants (*sańśa- > *säńśä?). The same conclusion though is suggested just as well by the distribution of the variants, and furthermore supported by our ability to reconstruct also other words that seem to pair as back/front variants of a single pre-Proto-Uralic root: e.g. *ńalə- ‘to lick’ ~ *ńälə- ‘to swallow’.
[1] More on this issue to come in a later blog post or three.
Freelance reconstruction 
Very interesting to read about the etymology of the Finnish ‘seistä/seisoa’ — I didn’t actually realize that there were two forms! I was trying to figure out if the two stems varied in terms of the several non-finite constructions in Finnish, from a syntactic perspective:
–the TA-infinitive: both forms
–the MA-infinitive: only ‘seisoa’ (seisomaan/seisomassa/seisomasta)
–the rationale construction: both forms (seistäkseen, seisoakseen)
–the temporal construction, present and past: both forms (seistessä, seisoessa; seistyä, seisottua)
–the infinitive you mentioned: both forms (seisten, seisoen)
The only other regularly used non-finite construction (at the sentence-level) is the
complement clause formed with the participial -VA (present) or -NUT (past):
Näin Jukan seisovan rannalla.
I-saw Jukka-GEN stand-VA/GEN beach-ADE
‘I saw Jukka stand(ing) on the beach’
The past tense form would be ‘seisseen’, both present and past with the ‘seisoa’ stem. Is the ‘seistä’ variant not possible here? I can’t figure out what the form would be.
[Moderator’s note: missing ääkköset added.]
If I’m reading this right — if you’re having trouble forming the seistä counterpart of seisseen, no wonder; it is already derived from seis-. Instead, its seisoa counterpart would be seisoneen. (Compare e.g. haista : haisseen ‘to smell’, paisua : paisuneen ‘to swell’.)