We review the parameter regions allowed by measurements of $\mathcal{R}({D}^{(*)})$ and by a theoretical limit on $\mathcal{B}({B}_{c}\ensuremath{\rightarrow}\ensuremath{\tau}\ensuremath{\nu})$ in terms of generic scalar and pseudoscalar new physics couplings, ${g}_{s}$ and ${g}_{p}$. We then use these regions as constraints to predict the ranges for additional observables in $b\ensuremath{\rightarrow}c\ensuremath{\tau}\ensuremath{\nu}$ including the differential decay distributions $d\mathrm{\ensuremath{\Gamma}}/d{q}^{2}$; the ratios $\mathcal{R}(J/\ensuremath{\psi})$ and $\mathcal{R}({\mathrm{\ensuremath{\Lambda}}}_{c})$; and the tau-lepton polarization in $B\ensuremath{\rightarrow}{D}^{(\ensuremath{\star})}\ensuremath{\tau}\ensuremath{\nu}$, with emphasis on the $CP$-violating normal polarization. Finally we map the allowed regions in ${g}_{s}$ and ${g}_{p}$ into the parameters of four versions of the Yukawa couplings of the general type-III 2HDM model. We find that the model is still viable but could be ruled out by a confirmation of a large $\mathcal{R}(J/\ensuremath{\psi})$.