  We explore semileptonic $B$ decays to the four lightest excited charm mesons,
$D^{**} = \{D_0^*,\, D_1^*,$ $D_1,\, D_2^*\}$, for nonzero charged lepton mass
and for all $b\to c \ell\bar\nu$ four-Fermi interactions, including calculation
of the ${\cal O}(\Lambda_\text{QCD}/m_{c,b})$ and ${\cal O}(\alpha_s)$
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 ${\cal
O}(\Lambda_\text{QCD}/m_{c,b})$ corrections can be very important. The $D^{**}$
rates exhibit sensitivities to new physics in $b\to c\tau\bar\nu$ mediated
decays complementary to the $D$ and $D^*$ modes. Since they are also important
backgrounds to $B\to D^{(*)}\tau\bar\nu$, the correct interpretation of future
semitauonic $B\to D^{(*)}$ rate measurements requires consistent treatment of
both the $D^{**}$ backgrounds and the signals. Our results allow more precise
and more reliable calculations of these $B\to D^{**}\ell\bar\nu$ decays, and
are systematically improvable by better data on the $e$ and $\mu$ modes. As an
example, we show that the $D^{**}$ rates are more sensitive to a new $\bar c\,
\sigma_{\mu\nu} b$ tensor interaction than the $D^{(*)}$ rates.
