Again comparing my map with notes I took and the View map option I think this was the Bouleuterion, which knew three periods. During the first it laid next to the theatron, steps along one side of the Bouleuterion were once part of that earlier theatron. This collapsed at some point, when rocks under it collapsed. So new seats were carved to the north of the former set of seats. The floor of the orchestra was raised. Later the theatron collapsed once again, for the same reason, and a new hall was built, stretching over part of the former with wooden columns on top of marble bases recycled from older buildings in town. The first phase was from Hellenistic times, the other two from the Roman period.

Note I may be completely wrong.