Hydrophobic cores are often viewed as tightly packed and rigid, but they do show some plasticity and could thus be attractive targets for protein design. Here we explored the role of different functional pressures on the core packing and ligand recognition of the SH3 domain from human Fyn tyrosine kinase. We randomized the hydrophobic core and used phage display to select variants that bound to each of three distinct ligands. The three evolved groups showed remarkable differences in core composition, illustrating the effect of different selective pressures on the core. Changes in the core did not significantly alter protein stability, but were linked closely to changes in binding affinity and specificity. Structural analysis and molecular dynamics simulations revealed the structural basis for altered specificity. The evolved domains had significantly reduced core volumes, which in turn induced increased backbone flexibility. These motions were propagated from the core to the binding surface and induced significant conformational changes. These results show that alternative core packing and consequent allosteric modulation of binding interfaces could be used to engineer proteins with novel functions.