  The KAPPA package is designed for calculations of optically thin spectra for
the non-Maxwellian \k{appa}-distributions. This paper presents extension of the
database to allow calculations of the spectra for extreme values of \k{appa} <
2, which are important for accurate diagnostics of the \k{appa}-distributions
in the outer solar atmosphere. In addition, two improvements were made to the
ionization equilibrium calculations within the database. First, the ionization
equilibrium calculations now include the effect of electron impact
multi-ionization (EIMI). Although relatively unimportant for Maxwellian
distribution, the EIMI becomes important for some elements such as Fe and low
values of \k{appa}, where it modifies the ionization equilibrium significantly.
Second, the KAPPA database now includes the suppression of dielectronic
recombination at high electron densities, evaluated via the suppression
factors. We find that at the same temperature, the suppression of dielectronic
recombination is almost independent of \k{appa}. The ionization equilibrium
calculations for the \k{appa}-distributions are now provided for a range of
electron densities.
