This paper explores the viability of established criteria to design centrifugal compressor stages that operate CO2 close to the critical point. The work is split into two complementary studies. At first, several stage configurations are generated by varying characteristic design parameters, such as the inlet and outlet flow coefficient, work coefficient, and stage Mach number. Then, three selected configurations are optimized with a surrogate-assisted evolutionary strategy to refine specific geometrical parameters, which control the meridional shape and splitter location. The stage aerodynamics and performance are assessed with a validated RANS solver based on the homogeneous equilibrium assumption for the two-phase mixture. One of the key findings of the parametric studies is that designing a stage with a flow coefficient smaller than that suggested by design practices prevents the occurrence of two-phase flows. The onset of a secondary phase at the impeller intake alters the fluid compressibility, producing density gradients across saturated condition that can cause flow separation. Such separation occurs for liquid-like CO2 but not for vapor-like CO2, implying that consolidated design rules can apply to the latter case notwithstanding the presence of condensing flows. Shape optimizations reveal that modest efficiency improvements can be gained by changing the meridional channel and splitter location. Moreover, the optimization problem is highly multimodal, as more than 30 different geometries can yield equivalent design efficiency. As a side effect of the optimization, the rangeability is significantly modified. Specifically, increasing the inlet slope angle of the shroud contour extends the operating range at high flow rates but reduces it at low flow rates. Therefore, this geometrical parameter can be controlled to adjust the stage rangeability without compromising design efficiency.