In previous works, the size-consistent self-consistent matrix dressing method has been applied to single reference as well as to complete active space singles and doubles configuration interaction. The wave function of the dressed state was assumed to be dominated by a closed shell determinant. Here, the method has been extended to systems where the dressed state is a single-configurational doublet. The method allows for the accurate calculation of energies and wave functions of other electronic states of the same system, having or not the same symmetry, as well as in the case of closed shell systems. This statement has been thoroughly assessed by the calculation of vertical ionization energies corresponding to a few low lying states of HF+ that are compared to full CI results obtained with the cc-pVDZ basis set. The method has been applied, using larger basis sets, to the calculation of vertical ionization potentials (VIP) of HF, H2CO, N-2, and NH3. The results are compared to experimental VIP values. The effects of selecting different CAS spaces and using pseudonatural adapted MO's obtained from the CASSCF matrix densities are shown and discussed. Mean absolute error (MAE) for the calculated states is about 0.07 eV. The difficulties to improve this precision limit are shown. However, the mean signed absolute errors, that measure accuracy, can be made smaller. Small MAE can be obtained using simultaneously VTZ basis sets and intermediate levels of calculation. The possibility of this effect to be assigned to a fortuitous cancellation of errors is pointed out.