  We show that, up to plausible uncertainties in BR$(B_c\to \tau \nu)$, the
$R_2$ leptoquark can simultaneously explain the observation of anomalies in
$R_{K^{(*)}}$ and $R_{D^{(*)}}$ without requiring large couplings. The former
is achieved via a small coupling to first generation leptons which boosts the
decay rate $\Gamma(\bar B\to \bar K^{(*)}e^+e^-)$. Finally we motivate a
neutrino mass model that includes the $S_3$ leptoquark which can alleviate a
mild tension with the most conservative limits on BR$(B_c\to \tau \nu)$.
