Speaking at the International Food Exhibition last month, Co-operative Group chief executive Peter Marks said he expected it would not be long before all of the societies joined the national brand.
"We now have 80% consolidation and the remaining 20% will soon follow. Watch this space," he said.
Plymouth & South West Co-operative Society, which has 67 food stores in Devon and Cornwall, said the "time was right" for the change, following the Co-op Group's £1.57bn acquisition of Somerfield.
Marks warned that jobs would be lost as part of the integration process, but added that the losses would take place at head office, not store level.
Marks also said that the Co-operative Group would not be looking to acquire any new stores in the immediate future. "We've got enough now to keep us going for a long time. I'm much less exercised by market share than I am about improving profits and sales."
Ethical credentials were now more important than ever, Marks added. "We have all seen where a system based on fear and greed takes us. So many big brands have been blown away recently because their leaders lost their moral bearings.
"Shoppers are now looking for brands that they can trust, and businesses which can deliver that trust will prosper."
Marks said the group would be revealing a "very significant increase in profits" when it announced its full-year financial results in May.