Could social enterprise benefit from using a co-operative identity?

Co-operative enterprises are extremely varied in their basis for membership, forms and structures, but all share a common global basis of shared values and principles to unite them.

To help reduce confusion about what type of co-operative they are, they group and identify themselves into a number of types, with each being based on their primary focus (type of member) – worker, housing, community, credit, consumer, ...

Maybe that’s a trick which the wider social enterprise movement might look to adopt in helping to reduce the ongoing confusion about what it is. Perhaps the basis for such ‘sub-grouping’ would be on their primary market or beneficiary, so we’d see ‘employment social enterprises’, ‘training social enterprises’, ‘health care social enterprises’, maybe even ‘co-operative social enterprises’?