Pinch Analysis is an effective technique to optimise Resource Conservation Networks (RCNs). These networks are widely used in process industries like petrochemical, pharmaceutical, and cement. Due to climate change, regulatory compliances, and market competition, process industries operate in epistemic conditions that impact their production efficiency and end-product quality. Process industries also use multiple resources to improve economic efficiency. Deployed RCNs must be designed to incorporate epistemic uncertainty while using multiple resources. Existing literature indicates that optimisation of RCNs using a single resource with epistemic parameters has been done. This work addresses the targeting of multiple resources present in RCNs, under an epistemic environment. Prioritized Cost formulation is extended to accommodate epistemic uncertainty by representing uncertain parameters using interval numbers. The proposed methodology identifies the parameter values favourable to utilising multiple resources. This methodology is illustrated through a case study on the solvent utilization network. The results from the case study demonstrate that adding another resource, under best-case condition, reduces total cost by 37.1 % from $ 40,580 to $ 25,516. Under worst-case condition, another resource is not required. An analysis of Prioritized Cost variation with different possible combinations of parameter values is presented using this case study.