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The interaction between the Staphylococcal Protein A (SpA) domain B (the basis of the Affibody) molecule and the Fc of IgG is key to the use of Affibodies in affinity chromatography and in potential therapies against certain inflammatory diseases. Despite its importance and four-decade history, to our knowledge this interaction has never been affinity matured. We elucidate reasons why single-substitutions in the SpA which improve affinity to Fc may be very rare, and also discover substitutions which potentially serve several engineering purposes. We used a variation of FoldX to predict changes in protein-protein-binding affinity, and produce a list of 41 single-amino acid substitutions on the SpA molecule, of which four are near wild type (wt) and five are at most a factor of four from wt affinity. The nine substitutions include one which removes lysine, and several others which change charge. Subtle modulations in affinity may be useful for modifying column elution conditions. The method is applicable to other protein-protein systems, providing molecular insights with lower workload than existing experimental techniques.