We examine a distributed control problem for internal flow management in a multi-zone climate unit. The problem consists of guaranteeing prescribed indoor climate conditions in a cascade connection of an arbitrarily large number of communicating zones, in which air masses are exchanged to redirect warm air from hot zones (which need to be cooled down) to cold zones (which need to be heated up), and to draw as much fresh air as possible to hot zones, relying on the ventilation capacity of neighbouring "collaborative'' zones. The controller of each zone must be designed so as to achieve the prescribed climate condition, while fulfilling the constraints imposed by the neighbouring zones - due to their willingness to cooperate or not in the air exchange - and the conservation of flow, and despite the action of unknown disturbances. We devise control laws which yield hybrid closed-loop systems, depend on local feedback information, take on values in a finite discrete set, and cooperate with neighbour controllers to achieve different compatible control objectives, while avoiding conflicts.