In this paper we present a novel distributed supervision strategy for networks of linear locally regulated and possibly dynamically coupled systems connected via data links and subject to coordination constraints on the evolutions of relevant variables of them. Such a coordination-by-constraint paradigm is accomplished by resorting to a Distributed Command Governor approach where each agent of the strategy 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 as that the global pointwise-in-time coordination constraints are satisfied along the overall network evolutions. A sequential strategy, where only one agent per time is allowed to manipulate its own reference signal, is fully described and analyzed. The constrained coordination of a network of dynamically coupled eight water tanks is presented as an example in order to show the effectiveness of the proposed method.