The finance committee of the Cambridge City Council last night recommended adding programs and personnel to the city budget for next year, a recommendation that could push the budget over the state-mandated four-per-cent tax cap.

The council will vote on the additions next week--if it approves more than $185,000 in addition to the budget, it will also have to override the cap, enacted by the state legislature at the insistence of Gov. Edward J. King last year, City Manager James L. Sullivan said last night.

More than $600,000 in additions were recommended by the committee last night. They include:

* $524,745 to pay for 25 new policemen to patrol the city's streets;

* $128,000 to expand Cambridge's "Just-A-Start" job training program;

* $49,000 for additional clerical personnel and hearing examiners for the city's rent control board;

* $28,000 for new roofs on two of Cambridge's branch libraries;

* and $1500 for a secretary for the city's committee on public planting.

Parsimony

Sullivan said last night that he would oppose all the additions except the recommended additional staff for the rent control board.

Under city law, Sullivan's opposition means that six councilors instead of a straight majority of five will have to favor each addition to the budget. Four of the additions, totalling more than $200,000, passed the finance committee with six or more votes last night, indicating that the final budget is likely to exceed the cap.

Only five councilors favored the most expensive item, the new policemen.

A six-member majority is also necessary to override the cap.

The committee voted down a total hiring freeze after some members complained that it might cripple small departments in the city government.

The council also refused to approve a more limited hiring freeze that would have applied only to departments with 50 or more employees. "That would be a gunshot way of making cuts. Across-the-board cuts indicate that those who propose them have not done their homework," Councilor Thomas W. Danehy said last night.

Councilor Saundra Graham, co-sponsor of the limited-hiring freeze plan, called it "a way of making people learn to do with less."

"The tax rate will go up not less than $30 and possibly as much as $50 next year," Councilor David Wylie, who also supported the limited freeze, argued. "This is a crisis of the first magnitude, and we have to do something about it," he said.