Computer simulation of a steady-state countercurrent multistage metal solvent extraction-stripping process (ESP) using cation-exchange reagents shows that there is a value of extraction equilibrium constant, K, yielding the maximum metal recovery when the other operational parameters are constant. Qualitatively, this is because the larger K makes stripping more difficult. Steady-state local linearization reveals the symbolic relation behind the numerical results. The coefficient of d(ln K) in the differential equilibrium relation extended to the countercurrent multistage process is the weighted average of the partial derivative, in each stage, of the equilibrium organic-metal molarity with respect to In K under constant equilibrium aqueous-metal molarity, where the weight is related to the partial derivative of the equilibrium organic-metal molarity with respect to the equilibrium aqueous-metal molarity under constant K. The balance of these coefficient values for the extraction and stripping sections of ESP determines the trend of the recovery with varying K : at the maximum recovery, these values are equal to each other. The stagewise plot of the partial derivative of the equilibrium organic-metal molarity with respect to In K under constant equilibrium aqueous-metal molarity versus organic-metal loading ratio clarifies the relation between the trend of the recovery with varying K and the organic-metal loading.