  The anomalies in the $B$-meson sector, in particular $R_{K^{(*)}}$ and
$R_{D^{(*)}}$, are often interpreted as hints for physics beyond the Standard
Model. To this end, leptoquarks or a heavy $Z'$ represent the most popular SM
extensions which can explain the observations. However, adding these fields by
hand is not very satisfactory as it does not address the big questions like a
possible embedding into a unified gauge theory. On the other hand, light
leptoquarks within a unified framework are challenging due to additional
constraints such as lepton flavor violation. The existing accounts typically
deal with this issue by providing estimates on the relevant couplings. In this
letter we consider a complete model based on the $SU(4)_{\rm C}\otimes
SU(2)_{\rm L}\otimes U(1)_{\rm R}$ gauge symmetry, a subgroup of $SO(10)$,
featuring both scalar and vector leptoquarks. We demonstrate that this setup
has, in principle, all the potential to accommodate $R_{K^{(*)}}$ and
$R_{D^{(*)}}$ while respecting bounds from other sectors usually checked in
this context. However, it turns out that $K_L \to e^{\pm} \mu^{\mp}$ severely
constraints not only the vector but also the scalar leptoquarks and,
consequently, also the room for any sizeable deviations of $R_{K^{(*)}}$ from
1. We briefly comment on the options for extending the model in order to
conform this constraint. Moreover, we present a simple criterion for all-orders
proton stability within this class of models.
