The transformation under way at San Francisco’s Stonestown Galleria is obvious these days. Gone are the bookend department store anchors, Macy’s and Nordstrom. A new Whole Foods is under construction, along with a Sports Basement, an expanded Target and an 11-screen Regal movie theater.

But mall owner Brookfield Properties doesn’t intend to rest after the current crop of businesses opens. Instead, Brookfield sees the new wave of retailers and entertainment venues as a prelude to a much bigger and more ambitious metamorphosis that would include a substantial number of new homes.

The potential foray into housing at Stonestown comes as mall owners around the Bay Area are looking to inject residential development into shopping centers, which tend to have vast surface parking lots on which to build. Mall owner Kimco has approvals to add 179 homes at Daly City’s Westlake Shopping Center and has proposed 303 homes at Fremont Hub. Brookfield has permission to add 1,500 homes at Newark’s NewPark Mall, which was struggling after losing major retailers.

Earlier this month, Brookfield held the first in a series of neighborhood meetings to gather feedback on what residents would like to see on the 40-acre Stonestown property.

Jack Sylvan, Brookfield senior vice president of development, said any future project there would include housing, but no decisions have been made beyond that. His group plans to meet with as many residents, businesses and community groups as possible over the next six months before submitting an application to the city in the spring.

“We have been honest with people,” said Sylvan. “The way to make a vibrant place is by adding a mix of uses, and that is definitely going to include housing.”

The possible Stonestown development comes amid increasing complaints that San Francisco’s west side is not producing its fair share of housing. The largest approved development on the west side, the addition of 5,679 apartments at Parkmerced, was approved eight years ago, but has yet to start construction, and there’s no timeline for breaking ground anytime soon. Given the size of the Stonestown site, it would likely be the second biggest housing proposal west of Twin Peaks.

At the meeting in early October, Brookfield executives were absorbing the concerns and hopes of 300 or so residents and others about traffic, parking and affordable housing. Brookfield representatives at the meeting declined to detail the number and location of the units.

But in a dense city with a housing shortage and scant available land, it’s likely that city planners will push Brookfield to create a significant number of units. The mall buildings occupy about 12 acres of the 40-acre site, leaving more than 28 acres of surface parking lots for redevelopment. In comparison, the city is proposing to add 1,100 units at the 17-acre Balboa Reservoir on Ocean Avenue, and a developer is set to start construction next year on 1,670 housing units at the 20-acre Schlage Lock site on the Brisbane border.

Supervisor Norman Yee, whose district includes Stonestown, said that he likes the idea of housing at the shopping center — but he has some reservations.

“They want to build housing, and I’m supportive,” said Yee. “But I want to make sure it’s appropriate housing and that there is a robust community process that addresses as many concerns as possible.”

Yee said any significant housing development would have to come with an investment in public transportation. Currently the city is looking at undergrounding the M-Ocean View Muni Metro line between West Portal and Parkmerced. That would double transit capacity on the line, which travels along the notoriously car-jammed 19th Avenue. The developer of the long-stalled redevelopment of Parkmerced has agreed to invest $70 million to improve the M-Ocean View.

In September, city officials started a $1 million study of that project.

“You can’t build the housing and not the transportation,” Yee said. “You can’t wait until after the housing is built.”

Planning Director John Rahaim said that Stonestown has “fantastic potential” for redevelopment, which could improve transit service and make the car-dominated streetscape more bike- and pedestrian-friendly. Housing would be a key part of the vision, he said.

“It seems to me that housing has to be part of the equation,” said Rahaim. “Between Stonestown and Parkmerced and San Francisco State, there is a great potential to think about how the M could better serve that part of the city.”

But opposition on the development-averse west side will likely be strong.

Brookfield is the fourth Stonestown owner to looking into redeveloping a portion of the property, which includes over 4,000 parking spaces. There was the 1997 proposal to replace Stonestown’s two-screen cinema with a 16-screen multiplex and erect a 900-car garage. Then in 2001, a different owner proposed expanded retail and a 414-unit housing development. Both of those developments died in the face of neighborhood opposition.

More recently, in 2008, then-owner General Growth Properties explored adding 70,000 square feet of retail, a six- to eight-screen movie theater and an expanded garage. That project was dropped during the recession.

Emily Murase, a former San Francisco school board member who lives across the street from Stonestown, said she would like to see housing for teachers and seniors, as well as job training programs and a mental health facility for teenagers.

While she said that many residents will likely oppose any new homes, the neighborhood is more open to change than it used to be.

“It can’t be business as usual with the housing crisis,” she said. “There is so much underutilized real estate around Stonestown.”

Sally Stephens, a west side neighborhood activist who lives about 2 miles from Stonestown in Golden Gate Heights, said that the first meeting on Stonestown was dominated by residents who “live nearby and don’t want any change.”

“But we are going to get housing somewhere on the west side — the only issue is where,” Stephens said. “I think (Stonestown) is one of the best places to put it.”

While retail is struggling around the country, Brookfield has pushed back against the notion that Stonestown is a “failed mall.” Sylvan said that the shopping center is doing quite well. It attracts 7 million visitors a year.

Over the past few years, the mall has become an Asian food draw, with new outlets selling boba tea, Japanese souffle pancakes, Taiwanese fried chicken and taro-filled buns. The new Whole Foods, Regal Theaters and Sports Basement are scheduled to open in mid- to late 2020. Target’s expansion will open in 2021.

Sylvan called Stonestown “one of the most diverse places in the city.” In addition to its proximity to San Francisco State University, the mall is a short walk from Lowell High School, Mercy High School and the Stonestown YMCA. It attracts groups of senior “mall walkers,” as well as families with kids from adjacent neighborhoods.

He said any redevelopment would likely feature places for gathering and live entertainment.

“At the end of the day, people are looking for places to gather and connect, and the retail has evolved to meet that demand, to the point where it’s as much about having an experience as anything,” said Sylvan.

Stonestown YMCA Director Joshua Leonard said adding housing would be “a positive for the Y and for the community.” He said YMCA staffers are hurt by the housing crisis and that he has already had informal talks with Brookfield about how it might become part of the redevelopment.

“Maybe there is a possibility for us to become part of a mixed-used development, or maybe a way for us to do programming or child care,” he said. “It’s really, really early, and we are in light discussions.”

Yee said so far Brookfield is taking the right approach — talking to as many people as possible before filing plans with the city.

“They seem to understand that nothing is going to fly if they don’t have a true community process,” he said.

J.K. Dineen is a San Francisco Chronicle staff writer. Email: jdineen@sfchronicle.com Twitter: @sfjkdineen