The objective of covering set location models consists in designing or modifying a network (commercial shops, antennas, drugstores, etc.) in order to cover totally or partially the demand related to a given area. When an area is covered by several activities (multi coverage), this can improve the responsiveness of the network (in case of congestion traffic for example) but this can also have negative effects such as customers’ cannibalization. In this paper, we propose an innovative covering set location model able to support decision makers to design networks that have a high resiliency level (i.e. ability to maintain service level despite hazards or failures) in a context of resources reduction (i.e. closing-down of network installations). Basically, the proposal allows studying the benefits and limits of multi coverage on each part of the network. Heuristic and exact methods are suggested to solve this problem.