At the heart of Proposition 10 is a straightforward question freighted with complex implications: Should officials in cities such as San Francisco be given more power to craft local rent control regulations.

Today, local lawmakers’ ability to shape rent-control policies is sharply restricted by the Costa-Hawkins Rental Housing Act. Prop. 10 would repeal that law and allow local officials to regulate rent increases and what kinds of dwellings would be subject to rent control.

And as Tuesday’s election approaches, some San Francisco lawmakers say they’re beginning to think about what rent control might look like if Prop. 10 passes.

The measure “unties our hands, so we can examine things that work and things that don’t work,” Supervisor Vallie Brown said.

Last month, Supervisor Hillary Ronen introduced legislation intended to address what Costa-Hawkins critics consider one of its most pernicious effects. Landlords are now permitted to raise a rent-controlled unit’s rent to market rate after the death of the unit’s “original tenant.” That can leave surviving family members and domestic partners facing huge rent increases. Ronen’s legislation — predicated on Prop. 10 passing — would allow surviving family members and partners to avoid those increases if they can prove they’ve lived in their unit for at least two years.

“This is one simple, slam-dunk piece of legislation that I believe would pass without much opposition in San Francisco,” Ronen said. “And it would allow us to protect residents in the worst moments of their life.”

Ending rent increases for surviving family members is also the first thing Brown wants to address if Prop. 10 passes.

“In the 3½ months I’ve been a supervisor, I’ve had two constituents that have lost their husband or wife, and then they get a letter from their landlord saying in 10 days or 30 days their rent is going up” because they weren’t the original tenant, Brown said. “That’s the thing I want to rectify. No decent person would disagree with that.”

In San Francisco, about 65 percent of households are renters, according to the city’s Planning Department.

Supervisor Aaron Peskin is supportive of Ronen’s legislation, but he has his sights set on an even bigger target.

Passed in 1995, Costa-Hawkins put limitations on local lawmakers that prohibit rent control on condominiums and single-family homes. It also prevents cities from limiting how much landlords can raise rents when a unit changes hands.

The law also prevents cities from extending rent-control protections to newer housing units. In San Francisco, rent control can’t be applied to any housing built after 1979 — the year the city’s laws were enacted.

Peskin said he’d aim to move up that cutoff date.

“Bringing that 1979 date somewhere around the end of the last century would make abundant sense,” he said. “I would say that if Prop 10. passes, the right thing to do is to bring a set of buildings built between 1979 and 1998 under rent control.”

Creating a rolling date for rent control and tweaking rules for surviving family members are “probably the two issues where we can build consensus at the board,” said Supervisor Rafael Mandelman.

Peskin authored a resolution the Board of Supervisors passed 9-2 last month endorsing Prop. 10. Supervisors Katy Tang and Catherine Stefani opposed the measure. Both declined to comment.

The wish list of Prop. 10 supporters on the Board of Supervisors overlaps with tenants’ rights activists. They’ve argued that Costa-Hawkins laid the groundwork for the city’s skyrocketing rents. Clearing the way for city officials to expand rent control is essential, they claim, to stabilize spiraling rental markets and tamp down the displacement they say rent hikes precipitate.

“Every time a rent-controlled unit gets demolished or burns down or gets Ellis-Acted — that’s a rent-controlled unit we lose forever. There are no new ones being created,” said said Deepa Varma, executive director of the San Francisco Tenants Union.

“We’d like to see buildings automatically fall into rent control after a certain number of years. That way, the developer gets to make whatever insane profits they want to make until things pencil out, and then those units get added to our rent-controlled housing stock,” she said.

Critics argue, however, that getting rid of Costa-Hawkins would dissuade housing developers from building new projects at a time when they’re needed the most.

Prop. 10’s opponents are particularly alarmed at the prospect of local lawmakers — or citizens via the ballot box — applying rent control to new construction projects.

Thanks to major contributions from real estate firms and property management companies, Prop. 10’s opponents have raised about three times as much as the measure’s backers. The nonpartisan Public Policy Institute of California reported last month that the measure was trailing in a statewide poll of likely voters 48 percent to 36 percent. The gap was even wider in the Bay Area, where opposition to the measure led 54 percent to 32 percent.

Many of the measure’s supporters know they’re in for an uphill fight on election day, but have vowed to continue to press the issue of expanding rent control in San Francisco.

“Repealing Costa-Hawkins is the great white whale of the California tenants’ rights movement,” said Shanti Singh, communications coordinator for Tenants Together in San Francisco. “If we don’t repeal it this year, we’ll try it the next year and the year after that.”

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