  We report a high-throughput ab-initio study of the thermodynamic and
superconducting proper- ties of the recently synthesized XB$_3$C$_3$
clathrates. These compounds, in which boron and carbon form a sponge-like
network of interconnected cages each enclosing a central X atom, are attractive
candidates to achieve high-Tc conventional superconductivity at ambient
pressure, due to the simultaneous presence of a stiff B-C covalent network and
a tunable charge reservoir, provided by the guest atom. Ternary compounds like
CaB$_3$C$_3$, SrB$_3$C$_3$ and BaB$_3$C$_3$ are predicted to exhibit T$_c$
$\lt$ 50 K at moderate or ambient pressures, which may further increase up to
77 K if the original compounds are hole-doped by replacing the divalent
alkaline earth with a monovalent alkali metal to form ordered $XY$B$_6$C$_6$
alloys.
