The article presents the results from numerically modeling the process circuit of a combined binary-cycle double-flash geothermal power plant (GeoPPs) with the use of secondary flash steam superheating by means of a hydrogen–oxygen steam generator. Geothermal heat carrier from substandard wells of the Mutnovsk geothermal field, as well as separated steam and waste brine from the Mutnovsk GeoPP, were taken as the primary heat source. Numerical investigation results have shown that the application of secondary flash steam superheating by means of a hydrogen–oxygen steam generator makes it possible to increase the steam turbine’s power output and its flow path efficiency owing to the steam wetness reduced by more than a factor of two. In addition, reduced steam wetness helps prevent erosion damage to the last-stage turbine rotor blades. Data on the effect that the use of different organic substances has on the efficiency and power output of the binary installation and of the GeoPP as a whole are given. Optimization investigations have shown that the highest power output and efficiency values of the binary installation used as part of a combined binary-cycle GeoPP at the lowest specific brine flowrate are achieved in using organic substances from the groups of nontoxic fire- and flame-proof (R-31-10 and RC-318) and low-toxic fire- and flame-proof ones (R-227ea, R-236fa, R1318, and R-134a) as working fluids. It has been established that the highest power output values of a combined binary-cycle double-flash GeoPP with secondary flash steam superheating by means of a hydrogen–oxygen steam generator are achieved in using the organic working fluids R-31-10, R‑227ea, and RC-318. In so doing, the optimum design pressure in the expander-separator at which the highest efficiency and power output of the studied GeoPP are obtained makes 0.47 MPa. In solving optimization problems on selecting the working fluids for binary combined-cycle GeoPP installations, it is proposed to use multiaxial composite diagrams of the relative values of geothermal power plant parameters and characteristics. An example of drawing a multiaxial composite diagram for the relative values of parameters and characteristics for a combined binary-cycle GeoPP for the R-290, R-31-10, R-32, and RC-318 working fluids is given. The numerical investigation results can be used in designing new and modernizing the operating GeoPPs that use steam geothermal sources.