  Time-dependent studies of inclusive charm decays to multibody self-conjugate
final states can be used to determine the indirect $CP$-violating observable
$A_\Gamma$ and the mixing observable $y_{CP}$, provided that the fractional
$CP$-even content of the final state, $F_+$, is known. This approach can yield
significantly improved sensitivity compared with the conventional method that
relies on decays to $CP$ eigenstates. In particular, $D \to \pi^+\pi^-\pi^0$
appears to be an especially powerful channel, given its relatively large
branching fraction and the high value of $F_+$ that has recently been measured
at charm threshold.
