  Evolutionary searches predicted a number of ternary phases that could be
synthesized at pressures of 100-300~GPa. $P6_3/mmc$ CaSH$_2$, $Pnma$ CaSH$_2$,
$Cmc2_1$ CaSH$_6$, and $I\bar{4}$ CaSH$_{20}$ were composed of a Ca-S lattice
along with H$_2$ molecules coordinated in a ``side-on'' fashion to Ca. The H-H
bond lengths in these semiconducting phases were elongated because of H$_2$
$\sigma\rightarrow$ Ca d donation, and Ca d$\rightarrow$ H$_2$ $\sigma^*$
back-donation, via a Kubas-like mechanism. $P\bar{6}m2$ CaSH$_3$, consisting of
two-dimensional HS and CaH$_2$ sheets, was metastable and metallic above
\edit{128~GPa}. The presence of van Hove singularities increased its density of
states at the Fermi level, and concomitantly the superconducting critical
temperature, which was estimated to be as high as \edit{$\sim$100~K at
128~GPa}. This work will inspire the search for superconductivity in materials
based upon \edit{honeycomb HX (X=S, Se, Te), and MH$_2$ (M=Mg, Ca, Sr, Ba)
layers} under pressure.
