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
Donald Trump has blamed 'radical Islamic terrorism' for UK's 13% rise in crime.
Theresa May said she is "ambitious and positive" for a Brexit deal as EU leaders gave the go ahead for preparations for second phase talks.
Merseyside Police have launched an investigation after crowd trouble at Goodison Park - during which a fan appeared to attack a player.