Single- and double-flash steam power plants are commonly used in the utilization of high enthalpy liquid-dominated geothermal resources. In these plants, the expansion line in the wet steam region results in significant penalties of turbine isentropic efficiency and power output. Accordingly, the “self-superheating” and “interstage heating” plant modifications have been recently proposed in the literature, where the saturated steam at turbine inlet is superheated by using the heat of the geothermal liquid, which is cooled before the flashing process. In this study, the aforementioned and additional new flash steam plant layouts are generated by using a systematic method, called Heatsep, for the optimum design of energy systems. All the thermal connections between consecutive basic plant components are “cut” to let these temperatures vary and in turn generate additional hot and cold streams, which are combined to enhance the overall performance of the system. It is demonstrated that the single-flash plant with self-superheating is simply obtained by cutting two out of five thermal links. In the double-flash plant, the higher number of components allows for a higher number of thermal cuts and heat integration options. Unlike the existing literature, the maximum power output is not constrained by a predefined heat transfer network. The optimization results show that the maximum power output of the novel single- and double-flash steam plants exceeds by 5.5–9.2% and 3.9–7.7% the maximum attainable by the corresponding traditional plants without internal heat integration.