  We generalize the relativistic field-theoretic three-particle finite-volume
scattering formalism to describe generic $DD\pi$ systems in the charm $C=2$
sector. This includes the isospin-0 channel, in which the recently discovered
doubly-charmed tetraquark $T_{cc}(3875)^+$ is expected to manifest as a pole in
the $DD \pi \to DD \pi$ scattering amplitude. The formalism presented here can
also be applied to lattice QCD settings in which the $D^*$ is bound and, in
particular, remains valid below the left-hand cut in $D D^*$ scattering, thus
resolving an issue in previous analyses of lattice-determined finite-volume
energies.
