The board of the Midcounties Co-operative, which operates gas and electricity supplier Co-operative Energy as well as Co-op branded food stores and other businesses, has voted against the proposals by former City minister Lord Myners.
These include a move to abolish the wider group's vast 21-member board, splitting it into two with a "plc" style panel responsible for commercial decisions and representatives from its traditional membership sitting on a separate body.
The Co-op group board has already agreed to this proposal but the shake-up still needs to be finalised and agreed by its millions of members.
It is the latest blow to the wider group after chief executive Euan Sutherland walked out claiming it was "ungovernable" - as he tried to push through reforms amid the worst crisis in the organisation's history.
The Co-op recently delayed the publication of annual results which are widely expected to reveal losses of £2 billion.
Warwick-based Midcounties Co-operative, which has 9,000 employees, 439,000 members who share in its profits, and gross sales of more than £1 billion, is the largest independent co-operative in the UK.
It says it is supportive of reform but is insisting that it is given a voice in discussions over the Co-op's future.
Its board voted against the Myners proposals on Monday night. They want more time to come up with a solution to protect the role of the members and the independent societies.
Midcounties president Patrick Gray told the Guardian: "If the group is simply presented with a menu that presents the Myners proposed position we will not support it."
A spokesman said: "The Midcounties Co-operative supports the view that reform is needed and is committed to working towards that.
"The Co-operative Group is a democratic organisation and we want to ensure that the views of our members and colleagues are fully represented during these very important discussions surrounding the future of the Group."
Lord Myners has said the group must take urgent steps to reform a "massive failure" of governance or it will go bust.
In an interim review published last month he criticised the lack of experience on its board and said he was "deeply troubled by the disdain and lack of respect for the executive team" among some members.
He acknowledged "acute concern" among Co-op board members and those in the regions over how reform could be achieved while preserving democracy, but said he was "confident that the two are fully compatible".
Lord Myners was appointed to the board in December and tasked with the independent review after a disastrous year for the Co-op in which its banking arm needed to be rescued following the discovery of a £1.5 billion hole in its finances.
It is now facing a series of investigations into what went wrong, as well as continuing questions over the appointment of disgraced bank chairman Paul Flowers despite a lack of knowledge of the sector. He was later exposed in a newspaper drugs sting.