A San Francisco supervisor has introduced legislation that will help more than 100 clubs and bars in the South of Market neighborhood — including the popular nightclub Mezzanine — keep their doors open amid mounting economic pressures that are threatening the area’s storied live entertainment spaces.

At a Thursday news conference convened at Mezzanine, Supervisor Matt Haney said his measure would force property owners to get a special permit if they want to transform west SoMa clubs or bars into office space — or anything other than an entertainment venue.

If passed by the Board of Supervisors, Haney’s measure would create added protections for nighttime entertainment spaces inside an area bounded by the southwest side of 12th Street to the southwest side of Fifth Street and the south side of Market Street to the south side of Harrison Street.

The measure would give the Planning Commission and, in some cases, the Board of Supervisors more opportunities to protect important cultural landmarks in the SoMa neighborhood, many of which are independently operated, Haney said. It wouldn’t prevent all conversions from entertainment to office space, but it would require property owners to jump through more hoops before making such a move.

Mezzanine was a fitting venue for the announcement: The Mint Plaza club has been operating on borrowed time since last year, after the building’s property owners said they planned to lease the space to a tech-office tenant and increase rent by as much as 600%.

“The only thing standing in the way of venues being displaced or pushed out is whether or not they have enough money to compete. Sadly, we are not going to win that battle most of the time,” Haney said.

“This is an independent venue. It’s a venue that’s woman-owned. It supports the community, it supports independent acts. It should not have to compete with big-tech office space in order to be able to stay here,” he added, referring to Mezzanine.

The venue’s situation became more dire this month, after owner Deborah Jackman announced that the building’s landlords withdrew a promise to extend its lease through January 2020, a move that would have forced the club to shutter by October. Jackman said she had already begun booking acts through the end of next January.

But on Wednesday there was reason for hope: The building’s owners called Jackman, saying they had reconsidered the decision to pull the lease extension. She anticipated signing an agreement to keep the club open until at least the end of next January.

“It gives me hope that they’ll come back to the table and potentially work out a long-term lease,” Jackman said.

The property is owned by the Chritton family, which operates a tech security business, Microbiz Security Co., out of the basement of the building. The family did not respond to a request for comment.

San Francisco resident Ashley Farwell said she worries about the trickling away of independent artists and the venues that provide platforms for their work, and she hopes Haney’s legislation will stave off further cultural erosion in SoMa. After moving on her own to the city a few years ago, she found at Mezzanine a group of like-minded music lovers who quickly became her social network.

“When we met, it felt like I had known them for years. There’s such a family vibe here and a huge spectrum of people,” she said. “We want to preserve our culture, and music is a huge part of our culture.”

Dominic Fracassa is a San Francisco Chronicle staff writer. Email: dfracassa@sfchronicle.com Twitter: @dominicfracassa