Government retirees who are already collecting a public pension could be allowed to work up to 30 hours a week at another taxpayer-funded job, under a legislative proposal that would ease the limits designed to curb “double-dipping.’’

The change, which has support in both the state House and Senate, would mark a dramatic jump for the 120,000 state and teacher retirees, and thousands of others who have left local government — hiking by as much as 50 percent the longtime limit on how many hours the former employees can still work in public jobs.

The Senate last week passed a measure that would increase the limit from 960 to 1,200 hours per year, pushing it to the equivalent of a 23-hour average workweek. The House went further, voting in April to hike the cap to 1,500 hours, which would allow retirees to work an average of 29 hours per week over a full year.

Lawmakers tacked the measures onto the chambers’ respective $41.5 billion budget plans, and Senator Michael J. Rodrigues, who filed the Senate version, said the final number of hours will probably “fall in between’’ when budget negotiators send the final version of the budget to Governor Charlie Baker’s desk.

Its potential passage is already causing consternation among some retirement officials who worry it creates a generous payday for those already collecting monthly taxpayer-funded checks from pensions.

“The law was on the books to prevent double-dipping,’’ said Kevin P. Blanchette, a former state representative who now serves as the chief executive of the Worcester Regional Retirement System. “With some of these folks, they retire early and go right back to work in the same job. It raises, for me, the question of, why retire then?’’

The current limit has for years been the focus of lobbying efforts by some retirees, who say the threshold is too low — namely former police officers who’ve sought out potentially lucrative detail work or retired fire chiefs who now help train firefighters. And amid tightening budgets at both the state and local level, fiscal watchdogs say the higher cap could provide a stopgap measure for towns or cities looking to fill a position without hiring a full-time employee.

But until now, their efforts hadn’t made headway, and bills never made it to the floor for a vote.

Representative Peter J. Durant, a Spencer Republican who filed the House amendment, said he pushed it after hearing from a constituent who is retired but wanted to work more hours as an adjunct professor.

The average state retiree’s pension is $36,587, while the average teacher’s is $45,683.

“People are always worried about the appearance of double-dipping,’’ Durant said. “But I think in 99 percent of the cases, that’s not the case. People just aren’t making enough in their retirement.’’

Paul D. Ford, the interim fire chief in Oxford, has lobbied Rodrigues personally, arguing that since retiring from the Brookline Fire Department in 2016 he’s had to continually turn down training requests at the Massachusetts Firefighting Academy or cut down his days as interim chief to stay under the 960-hour annual cap.

“I don’t see a reason for any restriction,’’ said Ford, who worked in Fall River for more than 28 years before going to Brookline.

Retirees can suspend their pension payments in order to return to full-time work in the public sector, but Ford said that “wouldn’t be financially reasonable’’ for him to do.

“Who benefits from this?’’ he said of the current cap. “Who gains with this law?’’

The Public Employee Retirement Administration Commission, which oversees the state’s public pension systems, has not yet reviewed the proposals and has not taken a formal position, according to executive director Joseph E. Connarton.

He said the current 960-hour limit was first set in 1981.

“It hasn’t moved in 37 years,’’ he said. “My guess is the Legislature is taking that into consideration.’’

Baker has the power to veto sections of the budget after lawmakers send it to him, which they’re expected to do later this summer.

Baker said Thursday that he wasn’t familiar enough with the amendments to give an opinion.

His administration has benefited from hiring back retirees, including hundreds of former state workers who left under an early retirement program but eventually returned in part-time roles, including some in six-figure positions.

Ensuring that retirees stay within their caps falls to the public entities who hire them. Beyond the hours limit, their salary is also limited, under the current rules. They can only earn the difference between the current salary of the position they retired from and their pension, a calculation that can differ from retiree to retiree.

But some retirement systems have also sought to recover payments from those they say earned beyond the limits. In Plymouth, local retirement officials have tried to recoup money from a former finance director, whose case set a precedent in 2014 that retired public employees cannot skirt the rules by creating a corporation to earn consulting fees.

Eileen McAnneny, president of the Massachusetts Taxpayers Foundation, a business-backed budget watchdog group, said lawmakers have to beware of unintended consequences but added the proposal could help.

She pointed to an “approaching retirement tsunami’’ in the public sector, in which cities, towns, and the state could use the new limit to tap “a talent pool that they wouldn’t have otherwise in this low unemployment environment.’’

Joshua Miller of the Globe staff contributed to this report. Reach Matt Stout at matt.stout@globe.com. Follow him on Twitter @mattpstout.