  We simultaneously incorporate two common extensions of the hadron resonance
gas model, namely the addition of extra, unconfirmed resonances to the particle
list and the excluded volume repulsive interactions. We emphasize the
complementary nature of these two extensions and identify combinations of
conserved charge susceptibilities that allow to constrain them separately. In
particular, ratios of second-order susceptibilities like
$\chi_{11}^{BQ}/\chi_2^B$ and $\chi_{11}^{BS}/\chi_2^B$ are sensitive only to
the baryon spectrum, while fourth-to-second order ratios like
$\chi_4^B/\chi_2^B$, $\chi_{31}^{BS}/\chi_{11}^{BS}$, or
$\chi_{31}^{BQ}/\chi_{11}^{BQ}$ are mainly determined by repulsive
interactions. 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. The modified hadron resonance gas model
presented here significantly improves the description of lattice QCD
susceptibilities at chemical freeze-out and can be used for the analysis of
event-by-event fluctuations in heavy-ion collisions.
