In recent work, a general superstructure and a Non-Linear Programming (NLP) model were presented for Multiple-Effect Evaporation Systems (MEESs). This NLP model was combined with a Heat Exchanger Network (HEN) model in order to simultaneously perform optimisation and heat integration of the overall system. The results of a forward-feed evaporation system integrated with hot and cold streams of the evaporation system as well as with the background process were presented. In this paper, the superstructure is extended by including multi-stage flash vessels for improving energy efficiency within the overall system. Additionally, various flow-patterns of heat-integrated MEES are studied. Also, trade-offs between energy and investment costs of heat-integrated MEES are explored for different numbers of evaporation effects in order to determine the optimum number of effects. The proposed Mixed-Integer Non-Linear Programming (MINLP) model of the combined MEES-HEN networks is implemented in a General Algebraic Modelling System (GAMS) and solved simultaneously using a two-step solution strategy. In the first step of the strategy, the NLP model of MEES is solved, providing an initialisation point for solving the MINLP model of the combined MEES-HEN network within the second step. A case study of a milk concentration process is used to illustrate the method. The results show that the forward feed flow-pattern with three evaporation effects is totally integrated with hot and cold process streams from the background process, and the system exhibits the minimum Total Annualised Cost (TAC).