SACRAMENTO — After failing to pass legislation to open up less densely populated parts of California to multifamily housing, state Sen. Scott Wiener is trying again with a “lighter touch” plan aimed at suburbs.

The San Francisco Democrat on Monday introduced SB902, which would essentially eliminate single-family zoning across the state by allowing multiunit housing in nearly all residential neighborhoods. Unlike his past effort, however, Wiener’s new proposal would cap the number of units that could be built in the smallest communities at two and limit the number in midsize cities to three.

The bill resurrects a provision of SB50, Wiener’s bill that also would have enabled taller, denser residential development around public transit and in wealthy suburbs. It failed on the Senate floor in January, after a similar proposal stalled in 2018.

Wiener said his new measure could significantly increase the housing supply in California while being mindful of preserving communities’ character. Local governments fiercely opposed his past legislation because they felt it failed to do that.

“It’s a much lighter-touch housing,” he said. “It’s OK for it be broader, because many communities in California that don’t necessarily have great transit or job access are still struggling with housing, and people are still hurting and becoming homeless and not being able to afford to live there. So we need housing everywhere.”

SB902 would create a right to build or convert homes into small multifamily housing in any residential neighborhood in the state, outside of areas at high risk of wildfires.

In unincorporated areas and cities up to 10,000 people, the bill would allow duplexes on any property. It would permit a building with up to three units in a city with between 10,000 and 50,000 people, and up to four units in a city with more than 50,000 people.

The legislation would not make changes to local height or design standards. That was a major source of anxiety for many opponents to SB50, who worried that it could radically change the look and feel of their communities by requiring cities to permit four- and five-story buildings near public transit.

But the new bill does create an option for cities to rezone residential parcels for apartment or condominium projects up to 10 units, without having to go through the formal environmental review that Wiener said can add five to 10 years to the process. Unlike his previous measure, allowing such construction would be up to cities — it would not be a state requirement.

The provision would apply to neighborhoods near public transit and in high-income areas with access to jobs and good schools. Cities could choose to adopt the change for any qualifying area through an ordinance.

“It will be much, much faster than the usual process,” Wiener said. “I hope we’ll signal to cities that we’re serious about giving cities more and more tools to make their lives easier in zoning for and approving more housing.”

SB50 also faced considerable pushback from affordable-housing advocates, who worried that it would accelerate gentrification by promoting luxury development. Wiener said the small projects covered by his new bill have different financial incentives and are less likely to lead to displacement, but he did include a provision that would prevent demolition of any home where a renter has lived in the past seven years.

The League of California Cities, which led opposition to SB50, declined to discuss Wiener’s latest proposal before its members had a chance to review the language. But the organization shared a “blueprint for more housing” that it released last week, which suggested that California should provide options for changes to local regulations. Among more than a dozen it suggested was “allowing up to fourplexes in single-family zones.”

Led by Senate President Pro Tem Toni Atkins of San Diego, the Senate Democratic caucus is working on a new housing production bill to replace SB50, which left the Democrats bitterly divided. That forthcoming measure could remove some of the urgency for Wiener’s SB902, though he said his bill would be complementary to whatever the Senate leadership comes up with.

“There is significant political space to make change and move the dial around housing this year,” he said.

Any policy that prescribes rules to local governments will nevertheless face a tough path in the Legislature.

Sen. Ben Allen, D-Santa Monica, voted against SB50 on the Senate floor in January, when it failed by three votes. He said Monday that he understood the “need to put pressure on communities” to increase housing construction, but said, “I’ve never been in love with unilateral upzoning.”

Allen said that while all options remain on the table, he would be looking for legislation that did not treat every city exactly the same and gave flexibility to those that are already building more housing.

“Shouldn’t they be allowed to do what they want to,” Allen said, “as long as they’re making a serious effort?”

Alexei Koseff is a San Francisco Chronicle staff writer. Email: alexei.koseff@sfchronicle.com Twitter: @akoseff