SACRAMENTO — Seeking to revive a fiercely fought bill that would boost construction of apartment buildings and condominiums, state Sen. Scott Wiener introduced changes Monday designed to disarm cities’ objections that the measure would remove their control over neighborhood character.

Wiener’s amendments would allow cities to opt out of certain provisions of SB50, his measure to increase housing around public transit and in wealthy suburbs, if they develop their own plans to build as many homes as the law would require. The changes would increase cities’ ability to keep some multi-unit housing out of neighborhoods that now consist of single-family homes.

But the key provisions of the bill remain intact: It would raise height limits around transit lines, allow denser development in high-income areas, and effectively open up the entire state to multifamily housing.

“I would love to see millions of homes come into California, like, yesterday,” said Wiener, a San Francisco Democrat. “We’re in a desperate, desperate state of affairs.”

In order to move forward in the new legislative session, SB50 must pass the Senate Appropriations Committee and then the full Senate by the end of January. Its prospects are uncertain.

Leaders at the state Capitol, including Senate President Pro Tem Toni Atkins and Gov. Gavin Newsom, have expressed their commitment to passing the measure in some form this year to address California’s housing shortage. But Democratic legislators representing suburban districts have been strong opponents.

State Sen. Anthony Portantino, the Los Angeles-area Democrat who chairs the Appropriations Committee, blocked the bill last year because of cities’ complaints about the potential loss of local control. His spokesman, Ben Edelstein, wrote in an email Monday that the amendments were not shared with Portantino, but “it was the senator’s hope that by taking a breath with SB50 it would focus efforts on actually building affordable housing as opposed to the market-rate housing predominant with SB50.”

Atkins, D-San Diego, said in a statement that she was “pleased there will be further consideration of this important measure” and expected there would be discussions to find a compromise that lawmakers could support.

Jesse Melgar, a spokesman for the governor, did not answer questions about whether Newsom supports the amendments. But he said in a statement that “the governor remains focused as a top priority on getting more housing built all across the state, for people at all income levels.”

Under the bill, local governments in counties with more than 600,000 people could not block residential buildings of at least four or five stories within half a mile of rail stations and ferry terminals, provided those projects meet other local design standards. In the Bay Area, San Francisco, Alameda, Contra Costa, Santa Clara and San Mateo counties meet that population threshold.

The measure would also remove density limits and reduce parking requirements within a quarter-mile of stops on bus lines with frequent service and in high-income census tracts with lots of jobs and good schools, regardless of their proximity to transit.

In smaller counties, including Marin, Sonoma, Solano and Napa, cities with more than 50,000 people would have to allow up to 15 extra feet of height for buildings within a half-mile of transit stops.

The changes that Wiener unveiled Monday would delay the start of the law until 2023, giving cities two extra years to come up with alternative plans that could accommodate the amount of new housing that SB50 would require. Those that did not would fall under the measure.

Wiener said he adjusted the bill after hearing from local officials who wanted more flexibility to build denser in some parts of their communities than others. But he said any plans they come up with would still have to meet SB50’s climate and fair-housing goals, and be subject to approval by the state housing department. That means they would have to meet targets for reducing car use and could not disproportionately push the new housing into low-income neighborhoods.

“SB50 will be extremely helpful to cities that are seeing a big increase in their housing goals,” Wiener said.

The League of California Cities, which was among those leading the opposition last year, said it still needed to review the changes but was “pleased to hear that the senator has been listening, and is amending his bill to reflect that feedback” from local government leaders.

Some local officials, including San Francisco Mayor London Breed and Oakland Mayor Libby Schaaf, are already on board.

Meghan Sahli-Wells, mayor of Culver City (Los Angeles County), said the measure is a “bold yet nuanced path” to address California’s climate and homelessness crises by building more housing where people work. Her city has about 40,000 residents, she said, but 60,000 jobs.

“The status quo is killing us,” she said.

Wiener’s bill has raised fears among affordable-housing and community groups that a building spree could drive vulnerable Californians out of their homes by speeding up gentrification.

The measure gives what Wiener called sensitive communities five years to come up with neighborhood plans that combine the development requirements with anti-displacement protections.

New apartment buildings and condominiums approved under the relaxed standards of SB50 would have to set aside 15% to 25% of their units for low-income families. In a change intended to keep poor residents from being forced out of their neighborhoods, people previously living within a half-mile of new developments would get priority for almost half of those low-income units.

Nearly everywhere in the state would be opened to multifamily housing through a streamlined process to convert vacant plots and existing homes in residential areas to apartment buildings of up to four units. That would essentially eliminate single-family zoning in California, except in small coastal communities and areas at high risk of fire.

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