The multiple-ionization energy difference of Ho163 and Dy163 atoms is evaluated for the ionization degree q=30,48,56. The calculations are performed by means of the large-scale relativistic configuration interaction method combined with the many-body perturbation theory. The quantum electrodynamics, nuclear recoil, and frequency-dependent Breit interaction corrections are taken into account. The obtained theoretical values are within 1 eV uncertainty. These results can help to increase the accuracy of the laboratory neutrino mass limit, provided they are accompanied by the corresponding experiment on electron capture in Ho and a precise measurement of the ion mass difference.