Those who support the model of the threefold distinction in PIE cite evidence from Albanian (Pedersen 1900) and Armenian (Pisani 1948), that they seem to treat plain velars differently from labiovelars in at least some circumstances, as well as the fact that Luwian could have had distinct reflexes of all three series.
It is disputed whether Albanian shows remains of two or three series (Ölberg 1976; Kortlandt 1980; Pänzer 1982), although the fact that only the worst—and one of the most recently—known (and neither isolated from external influences nor remote) IE dialect could be the only one to show some remains of the oldest phonetic system is indeed very unlikely. Clackson (2007), supporting the three series: “Albanian and Armenian are sometimes brought forward as examples of the maintenance of three separate dorsal series. However, Albanian and Armenian are both satem languages, and, since the *kj series has been palatalised in both, the existence of three separate series need not disprove the two-dorsal theory for PIE; they might merely show a failure to merge the unpalatalised velars with the original labio-velars.”
Supporters of the palatovelars also cite evidence from Luwian, an Anatolian language, which supposedly shows a three-way velar distinction *kj → z (probably [ts]); *k → k; *kw → ku (probably [kw]), as defended by Melchert (1987). So, the strongest argument in favour of the traditional three-way system is that the distinction supposedly derived from Luwian findings must be reconstructed for the parent Indo-Hittite language. However, the underlying evidence “hinges upon especially difficult or vague or otherwise dubious etymologies” (Sihler 1995); and, even if those findings are supported by other evidence in the future, it is obvious that Luwian might also have been in contact with satemising languages, that it might have developed its own satemisation trend, or that maybe the whole system was remade within the Anatolian branch, which is still poorly understood.
Additionally, one of the most difficult problems which subsists in the interpretation of satemisation as a phonetic wave is that, even though in most cases the variation *kj/k may be attributed either to a phonetic environment or to the analogy of alternating apophonic forms, there are some cases in which neither one nor the other may be applied, i.e. it is possible to find words with velars in the same environments as words with palatals.
Compare for example *okjtō(u) ‘eight’, which presents *k before an occlusive in a form which shows no change—to suppose a syncope of an older **okjitō, as does Szemerényi, is an ad hoc explanation. Other examples in which the palatalisation cannot be explained by the next phoneme nor by analogy are *su̯ekru- ‘husband’s mother’, *akmōn ‘stone’, *peku ‘cattle’, which are among those not shared by all satem languages.
Such unexplained exceptions, however, are not sufficient to consider the existence of a third row of ‘later palatalised’ velars (Bernabé 1971; Chen and Wang 1975), although there are still scholars who come back to the support of the hypothesis of three velars. So e.g. Tischler (1990), reviewed by Meier-Brügger (2003): “The centum-satem isogloss is not to be equated with a division of Indo-European, but rather represents simply one isogloss among many…examples of ‘centum-like aspects’ in satem languages and of ‘satem-like aspects’ in centum languages that may be evaluated as relics of the original three-part plosive system, which otherwise was reduced every-where to a two-part system.”
Newer trends to support the old assumptions include also Huld (1997), in which the old palatal *kj is reconstructed as a true velar, and *k as a uvular stop, so that the problem of the a priori unlikely and unparallelled merger of palatal with velar in centum languages is theoretically solved.