Tapping into demand for downtown Boston multifamily housing, Boston-based Cresset Development plans to convert three floors of a Chinatown building used as a telecommunications switching station into 46 apartments called the “PBX Residences.”

Cresset proposes 18 studios, 20 one-bedroom units and eight two-bedroom units in the top three floors of the Verizon building at 8 Harrison Ave., according to an application submitted to the Boston Redevelopment Authority last week.

Situated on a half-acre site, the 8-story building owned by Verizon was built in 1919 to house a telephone switching station. Cresset bought a condominium in March for $4.6 million, giving it a partial ownership stake in the 143,046-square-foot building, according to Suffolk County Registry of Deeds records.

The project would renovate the top three floors for apartments and the ground floor for a lobby and storage. Six affordable units would be included on-site. No on-site parking is proposed, requiring a variance from the Zoning Board of Appeals.

The project team includes Boston-based Bargmann Hendrie & Archetype Inc., Promontorio Architecture of Lisbon, Portugal and Kyle Zick Landscape Architecture of Boston.