A year ago, you may recall, the architecture firm Snohetta unveiled its initial plan to reincarnate the 37-story, 647-foot-high building with the Chippendale crown on Madison Avenue, between 55th and 56th Streets, which Philip Johnson completed in 1984 with his partner, John Burgee, for AT&T.

Snohetta’s big move in the first go around, visually speaking, was swapping out the lower portion of the building’s masonry facade for a diaphanous curtain wall. With its Apple store vibe, the fluted glass scrim exposed the building’s supporting steel structure and allowed light into a grand but gloomy second-floor sky lobby...