Twenty-four underused parcels of land in SoMa — most of which are parking lots — could be turned into affordable-housing projects, the San Francisco Board of Supervisors decided Tuesday.

An ordinance authored by Supervisor Jane Kim will allow the city to build 100 percent affordable-housing units in an area that was previously reserved for light industrial use. While all of the lots may not be suitable for housing, the Planning Department said the zoning change could lead to 600 or more 100-percent affordable units. The measure was passed unanimously by the board.

The zoning change comes as the board negotiates the details of the Central SoMa plan, which would revamp a portion of downtown San Francisco with 8,550 housing units and a projected 32,500 jobs. The plan, which has been widely criticized — even by Kim — for not including enough affordable-housing units, is working its way through the approval process.

“It is incredibly important to get every unit of affordable housing,” said Jon Jacobo, a legislative aide for Kim. “Especially with ... Central SoMa, the community needs every unit of affordable housing that it can get.”

Also at Tuesday’s meeting, the board took a big step toward expanding the city’s ability to compel homeless people suffering from debilitating mental illnesses or drug addiction into treatment.

Supervisor Rafael Mandelman and Mayor London Breed introduced legislation that would opt the city in to a new conservatorship pilot program under a new state law, SB1045. The proposal comes a month after Gov. Jerry Brown signed the bill by state Sen. Scott Wiener that gives San Francisco, San Diego and Los Angeles counties the ability to expand their local conservatorship laws.

“Introduction of this ordinance allows us to start a conversation that will no doubt take some time,” Mandelman said. “Because every day that San Franciscans suffer on our streets and in our jails from severe untreated substance-abuse disorder and mental illness is one day too many, a day that this government is failing.”

Tuesday’s introduction is the first step in the process of crafting the local policy. A plan is being developed with the Department of Public Health, the Department of Human Services, the city attorney’s office and other agencies on how to implement the program. Then the board will hold a hearing to determine whether the city has enough resources to treat people conserved under SB1045’s guidelines.

The board also approved an ordinance that would compel landlords of residential buildings that have received at least two fire safety violations to upgrade or install sprinkler and alarm systems.

Under the ordinance by Supervisor Hillary Ronen, the Department of Building Inspection and the Fire Department may order owners to upgrade problematic buildings without passing the cost of compliance on to their tenants.

Trisha Thadani is a San Francisco Chronicle staff writer. Email: tthadani@sfchronicle.com Twitter: @TrishaThadani