This work deals with the optimal synthesis, design, and operation of an integrated triple-pressure steam-reheat combined-cycle heat and power (CCHP) plant with a multiple-stage flash (MSF) desalination process to simultaneously generate electricity and produce freshwater from seawater. The study is performed using mathematical programming techniques and a generalized gradient-based optimization algorithm. A superstructure-based representation of the heat recovery steam generator (HRSG) of the CCHP embedding simultaneously several attractive candidate structures was proposed and a mixed-integer nonlinear programming model was derived from it. The model is developed in such a way that the number of the pressure levels in the HRSG is also included to the set of optimization variables. Series, parallel, and combined series-parallel heat exchanger arrangements and steam reheating are allowed. Depending on the demands of electrical power generation and freshwater production rate, HRSG structures involving three, two, or one pressure levels can be obtained as the optimal structure since the heat exchangers can be selected or removed from the superstructure accordingly. First-principle models of the involved equipment are used. In this work, the maximization of the ratio between the freshwater production rate and total HRSG heat transfer area is performed, while satisfying a fixed electrical power generation level. An existing dual-purpose desalination plant with a single-pressure HRSG is used as a reference case for model validation and result comparison.