Decoupling multiphase superconductivity from normal state ordering in CeRh2As2

${\mathrm{CeRh}}_{2}{\mathrm{As}}_{2}$ is a multiphase superconductor with ${T}_{\text{c}}=0.26$ K. The two superconducting (SC) phases, SC1 and SC2, observed for a magnetic field $H$ parallel to the $c$ axis of the tetragonal unit cell, have been interpreted as even- and odd-parity SC states, separated by a phase boundary at ${\ensuremath{\mu}}_{0}{H}^{*}=4$ T. Such parity switching is possible due to a strong Rashba spin-orbit coupling at the Ce sites located in locally noncentrosymmetric environments of the globally centrosymmetric lattice. The existence of another ordered state (phase I) below a temperature ${T}_{0}\ensuremath{\approx}0.4$ K suggests an alternative interpretation of the ${H}^{*}$ transition: It separates a mixed SC$+$I (SC1) and a pure SC (SC2) state. Here, we present a detailed study of higher-quality single crystals of ${\mathrm{CeRh}}_{2}{\mathrm{As}}_{2}$, showing much sharper signatures at ${T}_{\text{c}}=0.31$ K and ${T}_{0}=0.48$ K. We refine the $T\ensuremath{-}H$ phase diagram of ${\mathrm{CeRh}}_{2}{\mathrm{As}}_{2}$ and demonstrate that ${T}_{0}(H)$ and ${T}_{\text{c}}(H)$ lines meet at ${\ensuremath{\mu}}_{0}H\ensuremath{\approx}6$ T, well above ${H}^{*}$, implying no influence of phase I on the SC phase switching. A basic analysis with the Ginzburg-Landau theory indicates a weak competition between the two orders.