[WS:] What I had in mind is close to the concept of 'social economy' popular in EU and to some extent in Canada http://ec.europa.eu/enterprise/policies/sme/promoting-entrepreneurship/social-economy/
This entails enterprises that operate on the principles of solidarity and democratic governance - one person one vote as opposed one share one vote - but they operate like a regular business. This means they have to generate enough income from market sales to cover at least their expenses.
As to the relationship between this "social economy" and unions it is not fundamentally different from ordinary corporate ownership i.e. businesses are owned by holding companies that are in turn controlled by unions or consortia of unions. The holding company does not have to even be physically located in the state or even country where social economy establishments operate. The unions could provide "seed money" to establish or expand such social economy enterprises - it would certainly be a better use of union funds than forking them over to the Democrat party for which they get nothing in return.
Indeed, union dues is bupkes comparing to what capitalist corporations can bring to the political process, but these union dues can be "leveraged" by investments in 'social economy'. Every not-so bright schmuck graduating from a third rate business school understands what investment and leveraging is so I do not see why this should be an anathema to the left.
So to sum it up, the function of this 'social economy' would be three-fold. First, it would employment opportunities in a labor-friendly democratically governed environment. Second, it would generate economic resources that are derived from market rather than charity and that can be used to gain leverage in the political process i.e. by funding labor friendly political parties, labor friendly media, and labor friendly knowledge production. Third, is what can be termed the "legitimation function" - that providing pro-labor socialization experience for employees and customers, and also demonstration of an alternative economic model.
Of course, 'social economy' is not a substitute for a political party but rather a base that provides support for such a party or parties. The mode in which those parties operate would vary depending on the electoral system in a particular country. What seems most viable in the Etats Unis is a combination of either a "third" Labor party operating at a local or even state level in competition with both Democrats and Republicans, or a faction of the Democrat party in those states where Democrats are already labor friendly to a non-trivial extent (e.g. in Maryland). But the key word in the Etats Unis is LOCAL - do not pull a Nader, forget the POTUS, and try to elect labor representatives to local and state governments and to the Congress. But this is just a general idea rather than a blueprint for a political strategy which obviously depends on the reality on the ground.
Wojtek