The identification of optimal process parameters for the isolation of a target component from multi-component mixtures is especially challenging in industrial applications. With constantly increasing time to market pressure, screening a large parameter space is not feasible and design-of-experiment approaches with few experiments might fail due to dynamic and nonlinear reactions to small parameter changes. Model-based optimization can determine optimal operating conditions, once the model has been calibrated to the specific process step. In this work, parameters for the steric mass action model were estimated for the target protein and three impurities of an industrial antibody cation-exchange purification step using only chromatograms at different wavelengths and additional fraction analyses with size exclusion chromatography. Information on the molar or mass concentrations in the feed are not available. The model-based optimization results coincide with conventional chromatogram-based optimization.