Bradford Council has increased its plea for government financial help by £22m to avoid effective bankruptcy.
The under-strain authority is now asking for a total of £80m in this financial year, as well as £140m for 2024/25.
The cash would not be a bailout but would instead be borrowed, according to a new report which details "financial challenges on an unprecedented scale".
The government said it was "engaging regularly" with the council over its request.
Earlier this month, Bradford Council revealed it would be shedding more than 100 jobs as part of a £40m cost-cutting programme aimed at avoiding effective bankruptcy.
The measures also included closing three household waste centres at Ilkley, Queensbury and Cross Roads.
Further cuts are being planned to libraries and leisure centres.
A report by the council's new director of finance Steven Mair said the authority had applied for help from the government's Exceptional Financial Support programme, but was now having to increase its request by £22m.
The report said if the government agreed, the help would come in the form of a directive "which would allow the council to borrow to fund revenue expenditure up to an authorised limit".
Analysis: Aisha Iqbal, Radio Leeds political reporter
The authority is asking for Exceptional Financial Support from the government, but what that actually means is permission to bend the rules slightly - to borrow more and to sell off more of its assets.
This approach would apply a bit of balm to Bradford Council's financial wounds.
But is it actually just a sticking plaster solution?
Interestingly, on the day the council revealed its £22m plea, it also announced it’s doing a wholesale review of its leisure centres and libraries as it draws up a “hierarchy of provision”.
We know about the headline services already earmarked for the axe.
More will be revealed in a couple of weeks, when further details about the council’s budget proposals will be published.
It said the authority was facing a £75.5m overspend this year, which was an increase of £7.7m from the previous forecast three months earlier.
The council was planning to spend £48m of its reserves propping up this year's budget, so the real shortfall was more like £120m, the report said.
It said a growing number of councils across the country were reporting severe budget pressures and Bradford faced "financial challenges on an unprecedented scale".
Councillor Susan Hinchcliffe, leader of Bradford Council, said extra government funding for social care, which was announced earlier this month, would likely only amount to £5m for Bradford for one year only.
She said: "This is far lower than councils require to fund the rising levels of social need.
"Exceptional Financial Support is, therefore, the only route open to councils and that’s what we are negotiating now with government."
Ms Hinchcliffe said they were "being forced to look at all the services that we provide and make extremely difficult decisions about what we can continue".
She said officers were working on a five-year plan to make the council's finances more sustainable, which would be shared in due course.
The Department for Levelling Up, Housing and Communities has been approached for comment.
The department had previously said: "Since the council wrote to [us] requesting Exceptional Financial Support, we have been engaging regularly with them on their request.
“We stand ready to speak to any council that has concerns about its ability to manage its finances or faces pressures it has not planned for."