Seeking to add police officers, preserve shelters for homeless families and maintain low-cost bus service, the D.C. Council this week has started making tweaks to Mayor Vincent C. Gray’s $10.8 billion spending plan.

Council Chairman Kwame R. Brown (D) said Tuesday that his “number one objective” is to keep shelters open for homeless families and victims of domestic violence. Advocates testified Monday that Gray’s budget cuts threaten to shutter the only city-managed shelter serving families, except during cold weather, when the District is legally required to offer beds.

But Brown suggested that he would resist calls to reverse other cuts to social programs that Gray has proposed, including limits on cash assistance to families. He noted that the mayor used to run the city’s Department of Human Services in the early 1990s.

“If it was any other mayor that sent down these cuts, I might pause,” Brown said. “But I had to take a second and say, ‘You know, this is a man whose whole life has been in this area.’ So, the least I can do is say, ‘He’s put some thought into it.’ ”

In a parallel saga, council members are seeking to boost the number of city police officers, which under Gray’s budget plan would fall to nearly 3,700 by October 2012.

Police Chief Cathy L. Lanier has said she would have “trouble” policing the District should her force drop below 3,800 officers. A draft report issued by the council’s Committee on Public Safety and the Judiciary on Tuesday said that in light of Lanier’s position, “the sworn number simply cannot be permitted to reach a level that low.”

But the committee’s chairman, Phil Mendelson (D-At Large), was not able to find savings among the agencies under his committee to pay for the 3,900 officers he is recommending, and he suggested that his colleagues find an additional $10 million.

Brown said that he supports hiring enough officers to meet Lanier’s needs. “If we can get it to the number the chief recommends, we want to be able to do that,” he said. “I think the chief knows better than anyone.”

Other potential changes to Gray’s budget plan came from Tommy Wells (D-Ward 6), chairman of the public works and transportation panel. He wants to add about $6.2 million to the District’s Metro subsidy. The money would help maintain bus and rail service in the city in the face of a Metro shortfall. A $1.1 million boost to the city Transportation Department would keep Circulator bus fares at $1, rather than the $2 proposed by Gray, and $2 million in capital funding would add 40 stations to the wildly popular Capital Bikeshare network. “Sweepercams” — cameras mounted on street sweepers that identify drivers who do not obey weekly parking restrictions — would be preserved for $300,000.

That money would come from unspent funds and two other initiatives. Tickets for drivers who park illegally in residential zones carry a $30 fine, but Wells recommends increasing it to $60 for a vehicle’s third such ticket in a calendar year. Much of the rest would come from an increase in the price of residential parking permits. Gray has proposed raising the amount from $15 to $25; Wells is suggesting that a household’s first permit cost $35, with the second permit costing $50 and additional permits priced at $100 each. Residents 65 and older would pay $25.

Other council members have tweaked their agencies’ budgets to fund their priorities. Mary M. Cheh (D-Ward 3) is proposing to use $200,000 from the city technology office to “support programs to expand access to healthy foods in low-income neighborhoods.” Cheh is also proposing to continue a freeze on city employees’ salaries and bonuses.

Muriel Bowser (D-Ward 4), chairman of the Committee on Libraries, Parks and Recreation, wants to shift $500,000 in capital funding from a planned renovation of the Cleveland Park Neighborhood Library, in Ward 3, to a redo of the Lamond-Riggs branch in Ward 5, which is patronized by many Ward 4 residents. Bowser, who is up for reelection next year, is also asking the D.C. Public Library to study placing a library at a new development at Riggs Road and South Dakota Avenue NE and wants the Parks and Recreation Department to consider a new park or recreation center for the soon-to-be-vacated Walter Reed Army Medical Center site. Both locations are in Ward 4.

The recommendations are subject to passage by each committee, and they could again be modified by the full council. The council will take its initial vote on the budget May 25; the new budget will take effect Oct. 1.

Also Tuesday afternoon, Vincent B. Orange was sworn in as an at-large member of the council; earlier that day, the District’s Board of Elections and Ethics certified the results of April 26’s special election.

Orange (D) took his oath in a packed council chamber that included Gray and the other 12 members of the council — including Brown, whom he ran against for the chairmanship last year.

In his remarks, Orange said he and Brown had settled their differences in a meeting last week, which he said included a “cleansing process.”

“After that,” Orange said, “we found common ground and moved on.”