A Transbay district tower that would fund more than 300 affordable housing units at no cost to the city could be held up for years, a potential victim of San Francisco’s cap on the approval of new office space and the flood of big South of Market projects lining up for permits.

At 806 feet, 546 Howard St. would be the city’s fourth-tallest tower and the last major high-rise in the Transbay district, the former industrial area that now hosts the city’s tallest neighborhood.

The project has been in the works for three years and would include a 190-room five-star hotel, 165 market-rate condos and 325,000 square feet of office space, which has already been fully leased to the cloud computing giant Salesforce.

To fulfill its affordable housing requirements — the Transbay neighborhood plan requires that 40 percent of units in the area be below market rate — developers Hines, Urban Pacific and Goldman Sachs will fund the construction of 337 affordable units two blocks east on the south side of Howard Street, between Beale and Main streets. That project, which would be built by the nonprofit Mercy Housing, would also include 181 market-rate apartments.

But proposed office projects must compete for approvals under Proposition M, which limits the amount of office space allocated each year. Space is running out, prompting representatives of 546 Howard St., as well as other developers seeking approval, to champion their projects at a Planning Commission hearing on Thursday.

San Francisco voters passed Prop. M in 1986 amid a building boom that included the Transamerica Pyramid, then the city’s tallest building. Activists pushed back against the “Manhattanization” of downtown San Francisco and won restrictions on office growth.

Under Prop. M, the city can approve only 875,000 square feet of large office projects a year. Unused space is saved for future projects, but the bank has been depleted during the current building boom driven by tech giants like Facebook, Google and Uber that are hungry for space.

Currently, 2.9 million square feet are available under the Prop. M cap, but developers want to build nearly 9 million square feet, according to city data. That means the city will have to determine which projects can be approved right away and which will have to wait — it could be years — until more space is available.

“It’s not a simple problem and one I wish we didn’t have to face — but we do have to face it,” said John Rahaim, the city’s planning director.

A wave of office projects in the newly rezoned Central SoMa area are seeking approvals. They include 88 Bluxome St., which would replace the San Francisco Tennis Club with 850,000 square feet of office space and other uses, and the Flower Mart redevelopment, which calls for 2.1 million square feet of offices.

The Board of Supervisors is also considering an ordinance that would give a one-time 1.3 million-square-foot boost to the amount of office space allowed by Prop. M by reallocating office space that has been converted into housing. The measure wouldn’t require voter approval.

Delays in the 546 Howard St. tower also could complicate expansion plans for Salesforce, which is San Francisco’s largest private employer with 8,500 workers. It plans to grow that number to 10,000 employees or more. The company declined to comment.

At Thursday’s Planning Commission meeting, representatives of both Hines and Mercy Housing said the 546 Howard St. project deserves priority for approval.

Project attorney C.J. Higley, a partner with Farella Braun + Martel, touted how much affordable housing the tower would produce and noted the amount of office space in the tower is relatively small, about 10 percent of what is available under the Prop. M cap.

“The project is shovel-ready. All the technical studies are complete,” Higley said. “We are ready to begin work as soon as the project is entitled.”

Mercy Housing California President Douglas Shoemaker said the affordable housing component won’t require taxpayer subsidies. Other office projects typically pay fees or donate land for affordable housing, which requires public subsidies to build.

“This is a project that is entirely subsidized by market-rate development,” he said. “I don’t know of any other project in the pipeline that is going to deliver that much affordable housing without a public subsidy.”

Higley said the affordable housing would be built concurrently with the tower and that both projects would receive their occupancy permits at the same time.

The booming office market is a critical funding source for affordable housing and other community benefits such as parks and nonprofit space, but a slowdown in construction means fees are dwindling, which may exacerbate the city’s housing shortage.

Planning Director Rahaim proposed picking the projects based on how ready they are to break ground, rather than what sort of community benefits they would provide. Affordable housing advocates prefer prioritizing projects with stronger community benefit packages.

Rahaim said that the Central SoMa projects were proposed before 546 Howard St., which would support the city approving them first. The Central SoMa Plan study was begun in 2011 but passed just last year.

Meanwhile, 546 Howard St. has lagged behind other Transbay towers like Salesforce Tower and 181 Fremont, which are completed and occupied. Development of the site, also known as Parcel F, was stalled after a previous developer, Crescent Heights, dropped its plan to buy the site. Hines and its partners bought the site in 2016.

Christopher Thornberg, founding partner of Beacon Economics, said the Bay Area’s lack of housing is crippling the ability of companies outside of the tech sector to hire enough workers, prompting some to leave the region entirely. Construction giant Bechtel and health care supplier McKesson both recently relocated their headquarters out of San Francisco.

“When you refuse to build housing, tech grows at everyone else’s expense,” he said.

J.K. Dineen and Roland Li are Chronicle staff writers. Email: jdineen@sfchronicle.com roland.li@sfchronicle.com Twitter: @sfjkdineen @rolandlisf