Sophisticated approaches have been proposed to reduce material utilities such as water and hydrogen by designing resource allocation networks. For resource targeting, graphical methods have been developed for single quality material recycle/reuse. Up to now, systematic approaches to targeting fresh resources in a multi-contaminant material recycling network ahead of the detailed design are not readily available. This work presents a rigorous resource targeting procedure in the domain of multiple constraints (e.g. multi-contaminants). The problem is formulated as a resource-allocation superstructure model and modified to determine the model characteristics and obtain the optimal solution. These conditions are then transformed into a table and graphical forms to identify the minimum resource target. By inferring from the mathematical formulations, multiple cascades with individual contaminant/quality have to be analysed sequentially. The main issues are the identification of the proper assignment of material sinks or sources as well as their ranking into each cascade. An example is solved to illustrate the accuracy and applicability of the method. The method also provides insights into the problem as it could identify the limiting constraints for individual sinks.