A novel distributed coordination strategy is presented for networked, locally regulated and possibly dynamically coupled, interconnected systems. Such systems are assumed to be connected via data links and subject to pointwise-in-time global constraints on some relevant variables of them, to be enforced as a coordination goal along the overall system evolutions. Such a coordination-by-constraint paradigm is accomplished by resorting to a novel distributed multi-agent Command Governor (CG) approach where each agent is in charge to locally modify, whenever necessary and on the basis of a reduced amount of data exchanged with the other agents, the prescribed set-points to the regulated subsystems so that the coordination constraints are always satisfied. The strategy is described and its main properties analyzed, especially for what it concerns the stability, feasibility and Pareto optimality of the solution. A liveness analysis concerning the possible presence of undesirable Nash equilibria and/or deadlock situations is presented and a discussion on the scalability of the solution with the problem dimension is reported as well. The constrained coordination of a network of interconnected water tanks is presented as a final example in order to show the effectiveness of the proposed strategy.