Excellent inherent oxidation resistance is a prerequisite for the use of superalloys in many high-temperature applications. To achieve this goal, typically continuous alumina and chromia scale growths are assured through sufficient Cr and Al additions. Since the intended γ/γ′-microstructure of superalloys is only stable within a certain compositional window, the maximum concentrations of these protective scale forming elements are, however, dependent on the overall alloy composition. The latter is a severe drawback, especially for Co-rich superalloys, as for these the maximum content often is insufficient for reaching the desired continuous scale growth. In recent years, the addition of significant Ni levels was identified to improve the high-temperature oxidation properties in the case of simple model alloy systems. In this study, we compare the high-temperature oxidation behavior of two complex Co-rich multinary single-crystalline γ/γ′-strengthened superalloys that only differ regarding their Co/Ni ratios to the commercial Ni-base superalloy CMSX-4. Therefore, time-resolved isothermal gravimetric analysis (TGA) in synthetic air at 850 °C and 1050 °C for 100 hours, scanning electron microscopy analysis (SEM), and electron probe microanalysis (EPMA) were conducted. The results point out that a high Co-content beneficially affects the oxidation resistance at 850 °C, meaning that the Ni-base CMSX-4 is slightly outmatched by the Co-rich competitors. In contrast, at 1050 °C, the commercial (most Ni-rich) alloy performed best and, clearly, an increasing Co-content was identified to deteriorate the oxidation resistance. This temperature-dependent influence of the nominal Co/Ni ratio on oxidation resistance is shown to be especially pronounced for dendritic regions. Consequently, the latter could be identified to especially determine the overall oxidation kinetics.