In this paper, an extension of previous work performed for a system of two plants is presented. For a set of n plants, heat transfer leading effectively to energy savings occurs at temperature levels between the pinch points of supplying and receiving plants. In some cases, additional heat transfer in other regions is required to attain maximum savings. A systematic procedure, based on LP and MILP models, is used to identify energy-saving targets for the two forms of integration and find the location of the intermediate fluid circuits. Finally, the optimal location of these circuits allowing restricted operation is discussed. Alternative solutions exist, which allow flexibility for the subsequent design of the multipurpose heat exchanger network.