A special general meeting in Manchester will decide on proposals drawn up in the wake of a disastrous period last year when it racked up record £2.5 billion losses.
The plans include reform of the food-to-funerals group's board structure, with elected directors - including the likes of a plasterer, engineer and retired deputy head teacher - largely replaced by professional business people.
An earlier poll in May saw the key principles behind the changes win unanimous backing but they now face resistance by some within the co-operative movement.
More than 500 have signed a petition, launched by Co-operative Business Consultants and backed by film director Ken Loach, saying the reforms are "directly opposed to the co-operative principles of democratic member control".
The changes to the constitution will require the backing of a two-thirds majority. At their heart are plans for a slimmed-down board of 11 directors with "high standards of competence" to oversee its running.
The rest of the board would consist of an independent chairman, five independent non-executive directors and two executive directors including the chief executive.
Co-op chair Ursula Lidbetter earlier this month said the reforms represented "the final crucial step in delivering necessary change to restore the group and return it to health".
Some opponents say they are "alarmed" by a rule change preventing members from making further changes to the governance of the group, without the agreement of the board and, they say, "tying the hands of members for generations".
But others say the changes do not go far enough. Lord Myners has said they fall short of his proposals but acknowledged they "represent significant progress in the right direction".
The Institute of Directors said in response to the plans, published earlier this month, that without an entirely independent board "there remain concerns about how much independent oversight the board will be able to exercise'".
The proposals also include establishing a 100-member council to act as guardian of the group's values and to hold the board to account, as well as a move to one-member one-vote on key matters such as the election of directors and major transactions.
Last year saw the Co-op group endure the worst crisis in its 150-year history after it was dragged down by the near-collapse of its banking arm as it discovered a £1.5 billion hole in its balance sheet.
The crisis led to questions over the composition of the group's board which, at the time Lord Myners published his review in May, had 15 lay members including an engineer, a plasterer and a retired deputy head teacher.
The peer said it was apparent to him within 30 minutes of his first board meeting that not one member had the ability to address the complex issues faced by a group burdened with debts of £1.4 billion.
A separate report by Sir Christopher Kelly into the downfall of the Co-operative Bank found that the Co-op group had badly let down its millions of members by failing to provide "proper stewardship" of the lender.
It has now seen its stake in the bank fall from 100% to 20% after a rescue plan that saw bondholders including US hedge funds take majority ownership.
Last week the lender reported first-half losses had narrowed from £845 million to £76 million but said it had lost 38,000 current account holders amid a "hurricane of negative publicity".
The wider group reports half-year interim results on Thursday.