We perform a general model-independent analysis of b → cτντ transitions, including measurements of RD , RD∗ , their q2 differential distributions, the recently measured longitudinal D∗ polarization FD∗, and constraints from the Bc → τντ lifetime, each L of which has significant impact on the fit. A global fit to a general set of Wilson coefficients of an effective low-energy Hamiltonian is presented, the solutions of which are interpreted in terms of hypothetical new-physics mediators. From the obtained results we predict selected b → cτντ observables, such as the baryonic transition Λb → Λcτντ, the ratio RJ/ψ, the forward-backward asymmetries AD(∗), FB the τ polarization asymmetries PD(∗) , and the longitudinal D∗ polarization fraction τ F D∗ . The latter shows presently a slight tension with any new-physics model, such L that an improved measurement could have an important impact.