Herod rebuilt the Temple, and he also expanded the area of the Temple Mount and built its new retaining walls. That is the accepted view among historians, and it also appears to be the view of the Sages.
(Therefore the Second Temple in its final form is called by the Sages “Herod’s building”: “Whoever has not seen Herod’s building has never seen a beautiful building in his life.” See also Bava Batra 3b: he said to him—that is, Bava ben Buta said to Herod—“You have extinguished the light of the world, as it is written, ‘For the commandment is a lamp and the Torah is light’; go and occupy yourself with the light of the world”—that is, build the Temple—“as it is written, ‘And all the nations shall flow to it.’” The Sages saw this as a kind of partial repair for some of his evil deeds.)