San Francisco supervisors struck a deal Monday to support a controversial law that would expand the city’s ability to force seriously mentally ill people into care — but the plan will likely help only about five people.

The Board of Supervisors is expected to approve the legislation on Tuesday, following months of debate over how the city should deal with severely mentally ill people on the streets. The supervisors battled for months over the proposal. But even the legislation’s most ardent supporters say it isn’t the answer to the city’s broken behavioral health care system.

The proposal expands the definition of who is eligible for conservatorship, which is court-ordered mental health treatment. If it passes, the city can impose in-patient treatment on someone if they are severely mentally ill, addicted to drugs and have been taken to an emergency crisis unit — known as a 5150 hold — at least eight times in a year.

While the city’s Department of Public Health estimates the expanded law would help only about five people, the board was fractured over whether the city’s already clogged mental health care system could adequately help more patients.

But on Monday, some supervisors said it was a small step in the right direction.

Supervisor Rafael Mandelman, who originally co-sponsored the legislation with Mayor London Breed, said he was pleased with his colleagues’ support, but was “frustrated that it took this long and it was this much work for something that was so incremental.”

Some supervisors said they decided to support the legislation after seeing several minor amendments crafted by Supervisors Matt Haney and Norman Yee. One amendment would ensure that someone is offered a bed in a treatment facility before they are put into inpatient treatment, and offered a housing placement after they are ready to move on. Those guarantees could minimize long wait times for people locked in psychiatric wards, and lower the possibility of people being dumped back on the streets after treatment.

Another amendment would guarantee that a specialized care team is in place to offer the people voluntary services before they are forced into care.

None of the amendments, however, addressed a fundamental problem that some supervisors had with the legislation: It would add more people to an already clogged mental health care system.

About 600 people are currently under court-ordered inpatient and outpatient treatment in San Francisco. Some of those people have found themselves stuck in locked wards for weeks — and in some cases, months — longer than they should be, as they wait for a bed in a more appropriate treatment facility to open up.

Long wait times still concern Supervisor Hillary Ronen, originally one of the law’s main opponents. But she said the amendments — particularly the one that ensures housing is offered — persuaded her to support the law. Her support is a big shift from two weeks ago when she called the proposal “unworkable.”

Ronen said she also changed her mind after Breed pledged $50 million in next year’s budget to include more than 100 treatment and recovery beds for people suffering from mental health issues and substance abuse. She also touted her recently proposed ballot measure — co-sponsored by Haney — which has the ambitious goal of guaranteeing mental health care for all city residents.

“It’s a combination of all those factors together that are allowing me to change my position on this,” she said. But “I think it is such a minor law and it will have such a minor impact compared to the gravity of our problem.”

A proposed state law, SB40, which recently passed the Assembly, could increase the number of people eligible under the expanded conservatorship laws to up to approximately 55 people.

Supervisors Haney, Yee and Ahsha Safaí also said Monday that they would vote for the legislation. That makes eight votes confirmed to The Chronicle, including the other co-sponsors Supervisors Vallie Brown and Catherine Stefani, and Supervisor Aaron Peskin, who said he would support the legislation last week.

If Mandelman’s colleagues did not support the measure, he threatened to bring the issue to the voters on the November ballot. On Monday evening, some supporters were still trying to persuade their colleagues to vote for the legislation in an attempt to get unanimous support. The goal, they said, is to show unity.

“Our homelessness crisis calls out for bold, persistent experimentation,” he said. But, he added, it’s challenging when “San Franciscans are really divided.”

Trisha Thadani is a San Francisco Chronicle staff writer. Email: tthadani@sfchronicle.com Twitter: @TrishaThadani