Ehud Netzer, The Architecture of Herod, The Great Builder (Mohr Siebeck, 2006)
When Herod undertook the ambitious task of rebuilding the Temple and expanding the Hasmonean Temple Mount, the Antonia already stood at the northwest corner of the intended site. So Herod constructed the new enclosure and simply incorporated the Antonia into the larger Temple Mount by building around it and adding stairways to connect the Antonia to the two stoas that lined the northern and western walls of the Temple Mount. Josephus’s description supports this layout, saying that, “At the point where it [the Antonia] impinged upon the porticoes of the Temple, there were stairs leading down to both of them, by which the guards descended.” Only if the Antonia extended onto the Temple Mount platform would it make sense to speak of “impinged” porticoes and two connecting stairways. The stairs at far left in the drawing above and on are a third staircase that led from the Antonia down into the valley and predate the Temple Mount expansion.