  A robust variational approach is used to investigate the sensitivity of the
rotation-vibration spectrum of phosphine (PH$_3$) to a possible cosmological
variation of the proton-to-electron mass ratio, $\mu$. Whilst the majority of
computed sensitivity coefficients, $T$, involving the low-lying vibrational
states acquire the expected values of $T\approx-1$ and $T\approx-1/2$ for
rotational and ro-vibrational transitions, respectively, anomalous
sensitivities are uncovered for the $A_1\!-\!A_2$ splittings in the
$\nu_2/\nu_4$, $\nu_1/\nu_3$ and $2\nu_4^{\ell=0}/2\nu_4^{\ell=2}$ manifolds of
PH$_3$. A pronounced Coriolis interaction between these states in conjunction
with accidentally degenerate $A_1$ and $A_2$ energy levels produces a series of
enhanced sensitivity coefficients. Phosphine is expected to occur in a number
of different astrophysical environments and has potential for investigating a
drifting constant. Furthermore, the displayed behaviour hints at a wider trend
in molecules of ${\bf C}_{3\mathrm{v}}\mathrm{(M)}$ symmetry, thus
demonstrating that the splittings induced by higher-order ro-vibrational
interactions are well suited for probing $\mu$ in other symmetric top molecules
in space, since these low-frequency transitions can be straightforwardly
detected by radio telescopes.
