  We investigate a $\mathrm{SO}(10)$ grand unification scenario where the
complex 10-dimensional scalar multiplet, containing the Standard Model (SM)
Higgs boson, resides at the TeV scale altogether. The resulting low-energy
model is a 2-Higgs-doublet model augmented with two $S_1$-type leptoquarks. The
gauge-coupling unification is achieved with only one intermediate scale at
which the Pati-Salam gauge group is broken down to the SM. A
$U(1)_{\mathrm{PQ}}$ global symmetry is also introduced, with the corresponding
axion providing a solution to the strong CP problem while also being an
important dark matter candidate. The proton-destabilising couplings of the
light leptoquarks are forbidden by a discrete symmetry. We discuss how the
simultaneous explanation for the $R_{D^{(*)}}$ and $a_\mu$ anomalies comes
about in the model, and investigate its phenomenological implications.
