The 31-story building, once the headquarters of A.I.G., has windows all around and a shape suited to extra corner units. In a city with too little housing, it could hold 800 to 900 apartments.

The four-story building with 102 apartments and a rooftop deck will be the first built with Connect Housing Blocks, modular housing units assembled in a factory on Westerville Road.

In fact, developer John’s first project in Olympia was on the corner of Adams Street and Fourth Avenue, where he redeveloped the Cunningham Building. Since then, John has built about 500 ...