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

KAPPA: A Package for Synthesis of Optically Thin Spectra for the  Non-Maxwellian Kappa-Distributions. III. Improvements to Ionization  Equilibrium and Extension to Kappa < 2