For what it is worth, we present here the details concerning the names of the originators of the Mahāsaṅghika heresy, according to the various translations of Vasumitra.
Kumārajīva (T 2032) mentions three names only, which he identifies as bhikkhus, not groups. In the Tibetan translation by Dharmākara (Tanjur, Mdo. XC, 11) the same three names are mentioned. Paramārtha (T 2033) and Xuan-zang (T 2031) agree that there are four, which they say are groups. Let us get the easy ones out of the way.
The third name in all lists is 多聞, which stands for Bahuśruta. The Tibetan has Man-du-thos-pa, also standing for Bahuśruta.
The second name is rendered 因緣 ‘condition’ (pratyaya) by Kumārajīva; 外邊 by Paramārtha; and 邊鄙 by Xuan zang. The latter two phrases both mean something like ‘outsider, border-dweller’ (pratyantika). The Tibetan has Śar-phogs-pa (= clansmen?). Thus the Indic original for these is probably something like Pratyantika.
The first name is rendered by Kumārajīva as 能 neng, which is apparently a carving mistake for 龍 long = nāga. Xuan-zang has 龍象, which translates Nāga, and the Tibetan has Gnas-bstan-klu for Nāga. But Paramārtha has 大國, which renders something like Mahāraṭṭha. Thus all except Paramārtha agree on this name.
Paramārtha and Xuan-zang also mention a fourth group, 大德. This can stand for Sthavira, and so Lamotte has it. But it is obviously incongruous, for the Sthaviras are precisely the group who oppose the 5 theses. Lamotte gets around the problem: ‘It becomes apparent from a comparison between the versions that the Pañcavastu [five points] was opposed by the Sthaviras and adopted by three assemblies, those of the Nāgas, Prācyas or Pratyantikas and, finally, the Bahuśrutas.’ But the sources are not so clear. Paramārtha  says the four groups shared the heretical teaching, while Xuan-zang  says the 4 assemblies disagreed over the 5 points. Kumārajīva speaks only of three bhikkhus who taught the 5 points. It is in fact a pseudo-problem, for both Paramārtha and Xuan-zang use上座 for Sthavira, when they are contrasting the Sthaviras and the Mahāsaṅghikas. Clearly they are using 大德 to represent a different Indic name. This might be Mahābhadra, Mahāyaśas, etc.
There are many curious things about this list. None of these names are found, to my knowledge, in other lists of Aśokan teachers. None are referred to in the rest of Vasumitra’s treatise, with the exception of Bahuśruta, which is also the name of one of the Mahāsaṅghika sub-schools. The geography, in so far as it has any meaning, is also curious: the early Mahāsaṅghikas are usually believed to have been settled in the old Buddhist areas around Magadha/Vesālī; but Mahāraṭṭha is far to the south-west, and the name Pratyantika ‘border-dwellers’ similarly hints at a distant origin. These names simply appear, stark and uninformative.