  In this paper, we propose $\mathrm{CeCoIn_5}/\mathrm{YbCoIn_5}$ superlattice
systems as a test bed for the reduction of topological classification in free
fermions. We find that the system with quad-layer of $\mathrm{CeCoIn_5}$ shows
a topological crystalline superconducting phase with the mirror Chern number
eight at the non-interacting level. Furthermore, we demonstrate that in the
presence of two-body interactions, gapless edge modes are no longer protected
by the symmetry in the system with quad-layer, but are protected in the systems
with bi- or tri-layer. This clearly exemplifies the reduction of topological
classification from $\mathbb{Z}\oplus\mathbb{Z}$ to
$\mathbb{Z}\oplus\mathbb{Z}_8$.
