Heuristic optimization is used to find sustainable cogeneration steam power plants with steam reheat and supercritical main steam parameters. Design solutions are analyzed for steam consumer (SC) pressures of 3.6 and 40 bar and a heat flow rate of 40% of the fuel heat flow rate. The objective functions consisted in simultaneous maximization of global and exergetic efficiencies, power-to-heat ratio in full cogeneration mode, and specific investment minimization. For 3.6 bar, the indicators improve with the increase in the ratio between reheating and main steam pressure. The increase in SC pressure worsens the performance indicators. For an SC steam pressure of 40 bar and 9 feed water preheaters, the ratio between reheating and main steam pressure should be over 0.186 for maximum exergetic efficiency and between 0.10 and 0.16 for maximizing both global efficiency and power-to-heat ratio in full cogeneration mode. The average global efficiency for an SC requiring steam at 3.6 bar is 4.4 percentage points higher than in the case with 40 bar, the average specific investment being 10% lower. The Pareto solutions found in this study are useful in the design of sustainable cogeneration supercritical power plants.