© 2018 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP 3 . We explore semileptonic B decays to the four lightest excited charm mesons, D∗∗={D0∗,D1∗,D1,D2∗}, for nonzero charged lepton mass and for all b→cν four-Fermi interactions, including calculation of the O(ΛQCD/mc,b) and O(αs) corrections to the heavy quark limit for all form factors. In the heavy quark limit, some form factors are suppressed at zero recoil; therefore, the O(ΛQCD/mc,b) corrections can be very important. The D∗∗ rates exhibit sensitivities to new physics in b→cτν mediated decays complementary to the D and D∗ modes. Since they are also important backgrounds to B→D(∗)τν, the correct interpretation of future semitauonic B→D(∗) rate measurements requires consistent treatment of both the D∗∗ backgrounds and the signals. Our results allow more precise and more reliable calculations of these B→D∗∗ν decays and are systematically improvable by better data on the e and μ modes. As an example, we show that the D∗∗ rates are more sensitive to a new cσμνb tensor interaction than the D(∗) rates.