To tackle constrained HENS problems featuring split networks as the best design options, the MILP framework introduced in Part I has been generalized in such a way that the new formulation remains linear. Parallel arrangements were considered by allowing multiple preceding and succeeding units for each potential heat match. The proposed approach allows the design engineer to specify the feasible predecessors and successors for every unit as well as the heat exchangers with which it can be arranged in parallel. Such topology constraints on the network design are considered from the beginning. To this purpose, new structural conditions have been incorporated into the MILP problem formulation so as to generate the larger solution space resulting from using stream splitting. Moreover, additional sets of restrictions are also included to define the common exit temperature of a hot/cold process streams coming from a set of parallel units. Similar to Yee and Grossmann (1990), the mathematical formulation assumes (a) isothermal mixers, (b) a single exchanger over a split stream and (c) no stream by-pass. The generalized MILP,framework is the basis of a targetting algorithmic method that accounts for all topology conditions from the start to sequentially determine (a) the constrained utility usage target; (b) the stream pseudo-pinch temperatures to decompose the problem into smaller independent subproblems and (c) the network designs at the level of structure one-by-one going from the top to the bottom network. Four example problems involving five to seven process streams were succesfully solved in a reasonable CPU time.