The council's Cabinet will discuss proposals to nearly double its current workforce in its children's social care department next week.
The local authority was heavily criticised by Ofsted in a damning report in July, which rated its children's services inadequate and said that vulnerable youngsters were being left at risk.
Among the issues highlighted by the regulator were heavy workloads for staff, poor morale and an over-reliance on agency workers.
The council has since said that they have whittled down the average number of cases per social worker from above 30 to 25.
But with the number of referrals to children's services continuing to rise, new proposals suggest an extra investment of £4m, on top of £4.5m which has already been pledged since the Ofsted report was published.
It is recommended that newly qualified social workers should only take on 15 cases at a time, with more experienced staff dealing with up to 20.
A report which will go before councillors on Tuesday, says: "Though increasing the numbers of social worker and team manager posts in the structure brings with it challenges around the need to recruit and retain additional staff, it is also likely to make permanent recruitment and staff retention considerably more achievable.
"In summary, in order to put in place the sustainable improvements needed in social work practice in the borough, it is necessary to create the right workloads and spans of control for social workers and managers.
"There is no indication that volume in the service is likely to reduce. Failing to put in place the right operating environment in this regard is likely to have a negative effect on the improvement work needed, and continue to leave children vulnerable to harm without the right social work interventions."
Although the council is already trying to recruit more staff as part of its improvement plan, the corporate director of children's services recently admitted that the hiring process was going "slowly".
A government commissioner is currently reviewing the service and will report in late November.
He may suggest that the council keeps the service, if he is satisfied with the progress it has made, or demand that it is privatised or taken over by the government.
Coun Margaret Isherwood, cabinet member for children and young People, said: "We are committed to ensuring that the best possible services are provided for children and families in this district. We recognise that more social workers are needed in the locality teams to make this happen.
"We want to attract the very best professionals and ensure they have a manageable workload.
“At the Cabinet meeting we will be considering allocating this additional funding, to expand this part of the service and as part of the action plan.
“We are in the process of achieving an improvement plan to ensure that our children’s services are brought up to the standard our children and families need and deserve and we are determined to deliver this."