Multiple-effect evaporators (MEEs) are energyintensive equipment, used for increasing the concentration of the solution. In order to minimize its energy consumption, it can be integrated with the background process. Energy consumption can also be minimized by integrating MEE with thermo-vapor compressor (TVC). A significant energy saving can be achieved by simultaneously integrating the MEE, TVC, and the background process streams. The present study focuses on the optimal integration of MEE, TVC, and background process stream by appropriately selecting the TVC operating temperature and the MEE effect temperatures. Selection criteria of appropriate temperatures are rigorously derived in this study. Based on the mathematical results, a methodology is proposed and is demonstrated through two illustrative examples: a forward feed corn glucose system and a parallel feed desalination system. By selection of the optimal temperatures, energy consumption for corn glucose system is observed to be reduced by 42%, with additional reductions in annual cost of 34%. Similarly, for the desalination system, the external steam requirement and the cost of producing freshwater can be reduced by 54% and 39% through appropriate selection of temperatures.