SAN JOSE — A builder of affordable homes has bought a fraternity house a short distance from the San Jose State University campus, a deal that could help the developer create housing for people who were formerly homeless.

First Community Housing has bought the downtown site where the Sigma Nu Fraternity had been operating a house for its Zeta Iota Chapter, Santa Clara County property documents filed on Nov. 30 show.

“We have been exploring sites for supportive housing in downtown San Jose just based on the fact that this is where the homeless problem is most concentrated,” said Geoffrey Morgan, president of First Community Housing.

The three-story house is located on South 11th Street between East San Fernando Street and East San Antonio Street.

The building is now vacant after the university and the Sigma Nu Fraternity suspended the Zeta Iota chapter in July.

First Community Housing is an increasingly busy developer of affordable homes in the South Bay, including several projects in San Jose.

In the most recent deal pulled off by First Community Housing, an affiliate of the nonprofit corporation paid $5.6 million for the fraternity house, the property documents show.

First Community Housing is eyeing the development of 120 supportive housing units for the formerly homeless now that the nonprofit has completed its purchase of the Sigma Nu house.

The fraternity house property could become part of a larger site where the supportive housing development would spout. Morgan said the nonprofit is discussing the purchase of additional property adjacent to the frat house site.

“Well-managed supportive housing with good services provides the safest conditions possible for the recently homeless,” Morgan said.

New York City-based Local Initiatives Support provided a $5.6 million loan to finance the property purchase by Lighthouse at Grace, the affiliate of First Community Housing. Local Initiatives Support specializes in property loans for affordable housing builders.

San Jose-based First Community Housing is working on multiple affordable housing projects in or next to downtown San Jose. These include:

— The Villages at Roosevelt, a proposed complex that would consist of 125 affordable residences at 995 E. Santa Clara St.

— Roosevelt Park Apartments at 21 N. 21st St., consisting of 80 affordable residences.

— McEvoy Apartments at 280 McEvoy St., would contain 365 residential units and be built a short distance from the footprint of Google’s proposed transit village.

Google Endeavor, a unit of the tech titan, has provided $29 million in financing for the McEvoy Apartments.