  The $\rho(770)$ vector resonance, its radial recurrences, and the
corresponding P-wave $\pi\pi$ phase shifts are investigated in an unquenched
quark model with all classes of relevant decay channels included, viz.
pseudoscalar-pseudoscalar, vector-pseudoscalar, vector-vector, vector-scalar,
axialvector-pseudoscalar, and axialvector-vector, totalling 26 channels. Two of
the few model parameters are fixed at previously used values, whereas the other
three are adjusted to the $\rho(770)$ resonance and the lower P-wave $\pi\pi$
phases. Preliminary results indicate the model's capacity to reproduce these
phases as well as the $\rho$ mass and width. However, at higher energies the
phase shifts tend to rise too sharply. A possible remedy is an extension of the
model so as to handle resonances in the final states for most of the included
decay channels. Work in progress.
