  We consider a model in which each family transforms under a different SU(3)
color group. The low-energy effective theory is an extension of the Standard
Model, with additional color octet gauge bosons $G_H$ with mass $M$ that couple
preferentially to the third family quarks. We show that there are two distinct
regions of the model's parameter space in which we can simultaneously evade all
the current experimental constraints, one with $M \approx 250$ GeV and the
other with $M \gtrsim 600$ GeV. Within each allowed region, we can obtain a
correction to the $Zb\overline{b}$ vertex that is consistent with the slightly
high value of $R_b$ observed at LEP. We show that there are $\Delta B = 1$
operators in our model that can suppress the $B$-meson semileptonic branching
ratio $B_{SL}$ and the charm multiplicity per decay $n_c$ by enough to
reconcile the spectator parton model predictions with the experimental data. In
the non-supersymmetric version of our model, we can only obtain the desired
corrections to $R_b$, $B_{SL}$ and $n_c$ in different regions of the allowed
parameter space, while in the supersymmetric version, we can obtain all three
corrections simultaneously. We also discuss a strong-coupling limit of our
model in which the third-family quarks become composite.
