Tender documents on the government's contracts finder website show that the DfE is looking to recruit experienced figures to provide "operational and strategic advice, support and challenge" in Barnet, Kirklees, Reading and Worcestershire.
The decision to appoint a commissioner in Kirklees comes despite Eleanor Brazil being appointed to the post last November in the wake of services being rated inadequate.
She was asked to prepare a report by 31 March 2017 on whether alternative delivery arrangements are the most effective way of securing and sustaining improvement.
In June it emerged that Kirklees had begun receiving expert support from Leeds City Council, amid speculation that the local authority was set to take over running the department.
The documents reveal that in Barnet an "alternative delivery model" is already under consideration - but does not give detail on what form this could take. In Kirklees, Reading and Worcestershire, commissioners will be expected to "develop a model for future operational delivery".
"Commissioners will provide a clear and sustained focus on the areas for improvement and ensure independent oversight of progress in line with agreed improvement plans," the tender document states.
"In doing so commissioners are expected to supervise the programme of change that the authority has embarked on, to drive forward the improvements and implement close monitoring arrangements, and build on the work that has already taken place.
"Commissioners will report to ministers on progress with their delivery of improvement measures which will inform decisions about the nature of the Department's intervention."
The documents reveal that in Barnet, where children's services were rated "inadequate" earlier this month, the appointed commissioner will be required to carry out an initial three-month in-depth review of services.
"Barnet Council have been working with an improvement partner for the last 12 months which has conducted a diagnostic of its services and an improvement board is in place," the document states.
"In addition it has undertaken work to consider an alternative delivery model (ADM) for children's social care that includes a comprehensive business case."
"The commissioner for Barnet would need to consider both the council's current improvement activities and the plans for an ADM as well as any other alternatives to assess how to most quickly secure sustainable improvement for children's services."
In Kirklees, Reading and Worcestershire, the DfE says commissioners will help drive improvement and work with the council to "oversee the establishment of a preferred delivery model".
"The commissioners will play a high profile role in a challenging political and delivery environment," the document states.
"They will bring their extensive and proven skills in children's social care transformation to challenge and support the senior leadership of the council and its partners as they work to improve services and develop a model for future operational delivery."
A total of £346,000 has bene set aside for the contracts, £107,520 in Barnet, £48,960 in Kirklees, and £95,040 in both Reading and Worcestershire based on the estimated amount of time commissioners will be expected to work on each contract.
The closing date for applications is 31 July, with the contracts due to commence from 31 August.