From the helicopter, cooperatives are espoused in market socialism. Whether this is big enough to be considered a "third school" is probably veering on being primarily opinion-based. Also there are a lot of flavors of market socialism (as detailed on that page); as for Wolff's:
In the early 21st century, the Marxian economist Richard D. Wolff refocused Marxian economics giving it a microfoundational focus. The core idea was that transition from capitalism to socialism required the reorganization of the enterprise from a top-down hierarchical capitalist model to a model where all key enterprise decisions (what, how, and where to produce and what to do with outputs) were made on a one-worker, one vote basis. Wolff called them workers self-directed enterprises (WSDEs). How they would interact with one another and with consumers was left open to democratic social decisions and could entail markets or planning or likely mixtures of both.
And these particular choices are one way to solve the socialization "dilemma":
Fundamentally, there are two major forms of "social ownership". The first is society-wide public ownership by an entity or network of entities representing society. The second major form of social ownership is employee-owned cooperative enterprise, with the members of each individual enterprise being co-owners of their organization. These possibilities give rise to a socialization dilemma, faced by advocates of public ownership: if social ownership is entrusted exclusively to state agents, then it is liable to bureaucratization; if it is entrusted exclusively to workers, then it is liable to monopoly power and abuse of market position.
Additionally, there are two major forms of management or "social control" for socially owned organizations, both of which can exist alongside the two major modes of social ownership. The first variant of control is public management, where enterprises are run by management held accountable to an agency representing the public either at the level of national, regional or local government. The second form of social control is worker self-management, where managers are elected by the member-workers of each individual enterprise or enterprises are run according to self-directed work processes.
So it has been an issue long debated in the socialist camp.