  CeRh$_2$As$_2$, a non-symmorphic heavy fermion material, was recently
reported to host a remarkable phase diagram with two superconducting phases. In
this material, the two inequivalent Ce sites per unit cell, related by
inversion symmetry, introduce a sublattice structure corresponding to an extra
internal degree of freedom. Here we propose a classification of the possible
superconducting states in CeRh$_2$As$_2$ from the two Ce-sites perspective.
Based on the superconducting fitness analysis and the quasiclassical
Eilenberger equations, we discuss two limits: Rashba spin-orbit coupling and
inter-layer hopping dominated normal state. In both limits, we are able find
two scenarios that generate phase diagrams in qualitative agreement with
experiments: i) intra-sublattice pairing with an even-odd transition under
magnetic field, and ii) inter-sublattice pairing with an odd-odd transition
under magnetic field.
