Lincolnshire County Council has scrutinised the company’s performance since it began its £70 million IT, finance, HR and customer services contract in April 2015.
Serco’s contract had been beset by problems which led to the authority reconsidering their services.
In December 2016, hundreds of public sector staff were left unpaid following an IT error.
But members of the authority’s Overview and Scrutiny Management Board have endorsed an extension to most of the firm’s services.
A final decision on the service will be made by the council’s executive next week.
The five-year contract with Serco is due to expire at the end of March 2020.
Council officers have recommended that Serco, which employs 400 staff in Lincoln, continues providing IT, payroll, HR, customer services, exchequer services and adult care finance until the end of March 2022.
But some services will be taken on in-house such as Freedom of Information, complaints and information governance and the Agresso system administration.
County council chief executive, Keith Ireland, said he has confidence that Serco are the “right people” to deliver the contract.
“Services are about the equipment, the technology and the people,” he said.
“I think that the people at Serco are the right people.
“I have done a lot of work on this and I think that Serco are as good as anyone.”
Councillors on the scrutiny panel said they felt “great comfort” in the chief executive’s confidence in the company.
Coun Hugo Marfleet said he felt Serco’s contract will get better.
“It is encouraging where we have been and where we are now,” he said.
“Serco are keen, constantly learning and always developing.”
But, chairman of the scrutiny board, Coun Rob Parker, said that the council “has as much to do as Serco” on the contract.
“We have to get our house in order so they can deliver their part in the partnership,” he said.