The renowned philosopher and champion of the Jews, Philo, was son of Gaius Julius Alexander (Lysimachus) in Alexandria of Egypt. A more senior brother of Philo, also called Gaius Julius Alexander, is further identified in Acts 4:6 as a relation of the High Priest Annas (Ananus/Ananius).
The ancestry of Gaius Julius Alexander is uncertain. However, according to a very plausible theory by Kass Evans, he descended from Honias (father of an earlier Ananias), who was a Sadducee and the last High Priest of the old line before it was ousted by the Maccabees/Hasmoneans. Honias and Ananias subsequently became leading Generals under Cleopatra II & III in Alexandria of Egypt. In the Evans model, Gaius Julius Alexander was the second Alexandrian by that name in a succession from Ananias son of Honias. Both of these Alexanders however distinguised themselves by changing loyalty and supporting Rome in its conquest of Egypt. The third Gaius Julius Alexander in succession was Philo's brother. He was appointed by Rome as Alabarch (Governor) of all the Jews in Alexandria.
It seems likely then that the second Gaius Julius Alexander, as father of both Philo and the Alabarch Alexander, was one and the same as the High Priest Annas. Rivival of the priestly name Annas (Ananias, Hebrew Hanan) would then have been symbolic and signified the return of this fallen priestly line to power in Jerusalem. Annas had been appointed High Priest by the Roman governor Quirinius at the same time Archelaus son of Herod was deposed and exiled to France. His election then amounted to a check and balance on the power of the feuding Herodian house.
After nine years, Annas was removed as High Priest by another Roman governor, but his family continued to dominate the temple administration until its destruction, which was ironically carried out under supervision of Philo's nephew Tiberius Julius Alexander son of Alabarch Alexander. The infamous High Priest Caiaphas is thought to have been a son-in-law of Annas. Five other High Priests of the 1st Century were also considered part of his family. These included one named Theophilus, a variant of the name Philo. Another son, also named Annas, was responsible for putting James the Brother of Jesus to death.
A second nephew of Philo named Marcus Alexander married the Herodian princess Berenice sister of Agrippa II. Demetrius, yet another relation of Philo, married the Herodian princess Mariamne sister of Berenice. In contrast to Herodians, members of the family of Philo appear not only as Jews but as Roman officials. The father of Philo was placed in charge of the very lucrative customs administration of Rome in Egypt. Philo's nephew Tiberius Julius Alexander became a Roman Procurator.
Therefore, we might also expect that Marcus Alexander doubled as the Roman official Marcus Piso, renowned defender of wealthy Jews living in Delos. We must further expect that the Alabarch Alexander, his sons Marcus Alexander and Tiberius Alexander, as well as Demetrius, were among the five "sons of Annas" that held the office of High Priest at various times, however under the more Hebrew sounding names of John/Jonathan/Nathanael (a.k.a., Bartholemew, "son of Ptolemy"), Eleazar, Matthias, and Annas (all sons of Annas).
High Priest Annas was called the son of Seth (or Sethi). Nothing unfortunately is known about this man Seth/Sethi and so we are not able to fully confirm the family pedigree from this bit of information either. It seems likely however that Sethi was a Hebrew epithet of Philo's father Gaius Julius Alexander II. It also seems reasonable that this Alexander was better known in Israel as "Ptolemy" the Steward and Seal Bearer of Herod the Great, a man that Herod trusted as much or more than members of his own immediate family. Ptolemy was named Executor of Herod's will.
Both he and his prominent brother "Nicolaus of Damascus" continued to mediate Herodian affairs after the death of Herod, and were involved in settling the dispute between the Herodian princes Antipas and Archaelaus in 6 A.D. They were both highly regarded in Rome for their wealth and sagacity. As a safeguard to Roman control, the politically charged High Priesthood was taken away from the family of Herod and logically given to the "neutral party" of Ptolemy/Gaius Julius/Alexander (Sethi).
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