$R_2$ as a single leptoquark solution to $R_{D^{(*)}}$ and $R_{K^{(*)}}$

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$(B_c\to \tau \nu)$.