The bank is finalising plans to fill the capital gap and float on the stock market, which will force losses on investors ranging from pensioners to multibillion-pound hedge funds who bought its bonds.
The wider Co-op Group, which spans funerals, banking and supermarkets, recently insisted there is "no plan B" to saving the bank, which slumped to £709.4 million losses in the first six months of the year.
But a powerful group of bond investors has racheted up the pressure on the bank, instead proposing an alternative plan of converting more debt into shares.
Other investors are also agitating over millions of pounds of write-downs recently made by the bank, and argue the lender is inflating its losses to persuade them to back its turnaround.
City regulators are forcing the embattled lender to repair its balance sheet to survive future crises.
The Co-op's current fundraising plan for the bank involves hitting bondholders for £500 million, raising £500 million from selling its insurance businesses and issuing £500 million of fresh debt.
The Co-op said it considered all other options - believed to include a taxpayer bailout - but insisted its plan is ''fair'' and in the ''long-term interests of all stakeholders''.
Now a rebel group of bondholders which owns almost a third of the bonds slated to be hit has demanded the bank plug the capital hole mainly through converting debt into shares - possibly forcing the Co-op Group to relinquish control.
The rebel investor group, believed to be fronted by US hedge funds Aurelius Capital Management and Silver Point Capital, said its plan would allow the bank to meet regulators' capital demands and called for it to be given "serious consideration".
It has been reported that the vulture funds bought into the Co-op Bank's debt after its financial struggles were revealed, to give them a strong bargaining position in the rescue talks.
The investor group, which comprises institutions holding more than £60 billion of assets, added the Co-op has "incorrectly stated" that its plan is the only option to meet the Prudential Regulation Authority's demands.
It said: " Substantially all the required £1.5 billion would be raised by converting the bank's subordinated bonds and preferred stock into bank common stock."
The group, represented by financial advice firm Moelis & Co, did not say how much of the bank it wants in return or whether it will derail the rescue plans by voting against them.
The Co-op is not expected to release precise terms of the turnaround until October.
The vulture funds added they would be willing to fill any remaining capital shortfall, which they said would be small.
The group also called for the bank and its advisers to open its books to investors, and reveal the same information that has been given to the wider Co-op group.
The hedge funds hold 43% of the higher-ranking bonds slated to be hit in the turnaround. That means they hold about £405 million of the £1.3 billion of targeted bonds - about 31%.
The bank's woes have been blamed on soured corporate loans, many of which were acquired with its takeover of Britannia Building Society in 2009.
The Co-op Bank has 4.7 million customers and employs about 10,000 staff.