Former City minister Lord Myners wants to replace this with a slimmed-down "plc and beyond" structure staffed by professionally-trained directors.
The former Marks & Spencer boss was appointed a director of the Co-operative Group in December but announced he is to leave following this weekend's vote.
He has said it was apparent to him from the first time he attended a board meeting that not one of its members had the ability to address the complex issues faced by a group burdened with £1.4 billion of debt.
This weekend's ballot will be decided by representatives of its independent societies and affiliated organisations - who hold 22% of the vote - and others voting on behalf of its regional membership boards making up the remaining 78%.
More top news
ITV News returns to Bergen-Belsen with Bernard Levy, a Jewish British army officer who was only 19 years old when he liberated the camp.
Gogglebox star Dom Parker has suspected concussion after crashing during ski training for Channel 4 Reality TV show 'The Jump'.
The 18-year-old went missing in 1991, and her body has never been found.