The ionization of groups in proteins may sometimes involve a partial unfolding and/or water penetration. Unfortunately the corresponding structural changes might not be captured by microscopic free energy perturbation (FEP) approaches due to activation barriers that are not surmounted in nanosecond FEP simulations. This problem is apparent, for example, from mutation experiments that introduced ionizable groups in protein interiors and from the difficulties to reproduce the corresponding pKa changes by microscopic approaches. Here we develop a new general approach for treating such challenging cases. Our approach drives the protein structural change by increasing the charge of the ionized group beyond its physical value and thus overcoming the barriers for the partial unfolding by a physically consistent process. The potential of our approach is illustrated by the evaluation of the pKa of the Val66Glu mutant of staphylococcal nuclease. In this case it is first demonstrated that standard FEP approaches give extremely disappointing results for this pKa. On the other hand, our "overcharging" approach gives a much more realistic result. We believe that the present approach represents a breakthrough in FEP studies of ionizable residues in proteins, and expect this strategy to be useful in studies of a wide range of challenging problems including simulations of hydrogen exchange processes.