There is no general agreement on the Julio-Claudian genealogy, despite the supposed Roman inforcement of monogomous marriage. Rather the Roman elite are reproducing very much in the old style of the pharaohs. The designations Antonia major and minor may just be a way of separating out the two families of a single woman, Salome sister of Herod the Great/Iullus Antonius. In Roman sources, she has only one husband, which is all that is allowed by law. The "slave man" seems equivalent to "common prostitutes" that bore children for the leading males. By Nero Drusus she bears Claudius, Germanicus and dau. Livillus (according to D. Shotter, 'Tiberius Caesar').
Josephus allows Salome sister of Herod the Great three husbands.
By the Idumean Costobarus/Ahenobarbus she has Berenice, Antipater, and an unnamed daughter. Berenice in turn becomes mother of Agrippa, Herod of Chalcis, Aristobulus, and Herodias. By the "Temple Treasurer" Helcias/Alexas (Freedman Alexander?) she bears another Helcias, who also becomes "Temple Treasurer". No children are attested by a third husband "Joseph"? (Need to revisit Josephus on this.)
The two families don't seem to overlap precisely, but perhaps Claudius was one and the same as Antipater son of Salome. Antipater married a princess Cypros (Valeria?), who in turn was the mother of a second Costobarus (Britannicus?) and another Cypros (Octavia?). And perhaps Germanicus was one and the same as Helcias son of Helcias/Alexas.
The single daughter would then correspond to Livilla, who was married off to a Drusus. This daughter was married off to her half-brother Helcias son of Helcias (who is logically one and the same as Germanicus, who she perhaps had children by - before or after the death of Drusus - under the name Agrippina!). The unnamed daughter (Livilla/Agrippina) became the mother of yet another Helcias/Alexas and another Antipas. These princes would correspond to the Roman Gemellus and/or sons of Germanicus, such as Nero Caesar, Drusus Caesar and/or Caligula.
Claudius then emerges as a very close relative of Agrippa, and one that reasonably would have "grown up" with him in an extended family living arrangement. We are dealing with a multiple husband/partner (Egyptian "God's Wife"/Queen Bee) model.
The identity of Antonia (major and/or minor) as the daughter of Antony and Octavia certainly explains the influence she had (under the name Salome) in the court of her half-brother Herod/Iullus Antonius.
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