In the last few years, the ratios RD(∗) and of RK(∗) have reportedly exhibited significant deviations from the relevant standard model predictions, hinting towards a possible violation of Lepton Flavor Universality and a window to New Physics. We investigate to what extent the inclusion of R-parity violating couplings in the minimal supersymmetric standard model can provide a better fit to the anomalies simultaneously. We perform this analysis employing an approximate, non-abelian Gf=U(2)q×U(2)ℓ flavour symmetry, which features a natural explanation of the appropriate hierarchy of the R-parity violating couplings. We show that, under the requirement of a supersymmetric spectrum with much heavier left-handed doublet superpartners, our assumption favors a considerable enhancement in the tree-level charged-current B→D(∗)τν¯¯¯, while the the anomalies induced by b→sℓ+ℓ− receive up to an approximate 30% improvement. The consistency with all relevant low-energy constraints is assessed.