  Coupling between Standard Model particles and theoretically well-motivated
ultralight dark matter (UDM) candidates can lead to time variation of
fundamental constants including the proton-to-electron mass ratio $\mu\equiv
m_{p}/m_{e}\approx1836$. The presence of nearly-degenerate vibrational energy
levels of different character in polyatomic molecules can result in
significantly enhanced relative energy shifts in molecular spectra originating
from $\partial_{t}\mu$, relaxing experimental complexity required for
high-sensitivity measurements. We analyze the amplification of UDM effects in
the spectrum of laser-cooled strontium monohydroxide (SrOH). SrOH is the first
and, so far, the only polyatomic molecule to be directly laser cooled to
sub-millikelvin temperatures, opening the possibility of long experimental
coherence times. Because of the high enhancement factors
($\left|Q_{\mu}\right|\approx10^{3}$), measurements of the
$\tilde{X}\left(200\right)\leftrightarrow\tilde{X}\left(03^{1}0\right)$
rovibrational transitions of SrOH in the microwave regime can result in
$\sim10^{-17}$ fractional uncertainty in $\delta\mu/\mu$ with one day of
integration. Furthermore, ultracold SrOH provides a promising platform for
suppressing systematic errors. More complex SrOR radicals with additional
vibrational modes arising from larger ligands R could lead to even greater
enhancement factors.
