  In previous work, we have developed a relativistic, model-independent
three-particle quantization condition, but only under the assumption that no
poles are present in the two-particle K matrices that appear as scattering
subprocesses. Here we lift this restriction, by deriving the quantization
condition for identical scalar particles with a G-parity symmetry, in the case
that the two-particle K matrix has a pole in the kinematic regime of interest.
As in earlier work, our result involves intermediate infinite-volume quantities
with no direct physical interpretation, and we show how these are related to
the physical three-to-three scattering amplitude by integral equations. This
work opens the door to study processes such as $a_2 \to \rho \pi \to \pi \pi
\pi$, in which the $\rho$ is rigorously treated as a resonance state.
