  We investigate extensions of the Hadron Resonance Gas (HRG) Model beyond the
ideal case by incorporating both attractive and repulsive interactions into the
model. When considering additional states exceeding those measured with high
confidence by the Particle Data Group, attractive corrections to the overall
pressure in the HRG model are imposed. On the other hand, we also apply
excluded-volume corrections, which ensure there is no overlap of baryons by
turning on repulsive (anti)baryon-(anti)baryon interactions. We emphasize the
complementary nature of these two extensions and identify combinations of
conserved charge susceptibilities that allow us to constrain them separately.
In particular, we find interesting ratios of susceptibilities that are
sensitive to one correction and not the other. This allows us to constrain the
excluded volume and particle spectrum effects separately. Analysis of the
available lattice results suggests the presence of both the extra states in the
baryon-strangeness sector and the repulsive baryonic interaction, with
indications that hyperons have a smaller repulsive core than non-strange
baryons. We note that these results are interesting for heavy-ion-collision
systems at both the LHC and RHIC.
