  We propose a nonperturbative resummation scheme for the four-point connected
quark-antiquark Green's function $G^4$ that shows how the Bethe-Salpeter
equation may be `unquenched' with respect to quark-antiquark loops. This
mechanism allows to dynamically account for hadronic meson decays and
multiquark structures whilst respecting the underlying symmetries. An initial
approximation to the four-point Schwinger-Dyson equation -- suitable for
phenomenological application -- is examined numerically in a couple of aspects.
It is demonstrated that this approximation explicitly maintains the correct
asymptotic limits and contains the physical resonance structures in the near
timelike region in the quark-antiquark channel whereas no resonances are found
in the diquark channel, respectively.
