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In this paper we provide an extension of maxmin fairness to the case of multiple objectives and different agent preferences by the definition of the maxmin multi-fairness relation. This generic relation is based on a formal modification of maxmin fairness according to its implicit comparisons and includes maxmin fairness as a special case. The application of this multi-fairness relation to a selfish, to a collaborative and to a mixed community of agents is presented, as well as a case study on a specific task of fair division of indivisible goods by numerical simulations. All studies demonstrate the suitability of the proposed relation for investigative tasks in shared resource problems, as they are abundant in network design and control.