  Recently, evidence has emerged for a field-induced even- to odd-parity
superconducting phase transition in CeRh$_2$As$_2$ [S. Khim et al., Science 373
1012 (2021)]. Here we argue that the P4/nmm non-symmorphic crystal structure of
CeRh$_2$As$_2$ plays a key role in enabling this transition by ensuring large
spin-orbit interactions near the Brillouin zone boundaries, which naturally
leads to the required near-degeneracy of the even- and odd-parity channels. We
further comment on the relevance of our theory to FeSe, which crystallizes in
the same structure.
