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 approximate to 250 GeV and the other with M greater than or similar to 600 GeV. Within each allowed region, we can obtain a correction to the Zb(b) over bar vertex that is consistent with the slightly high value of R(b) observed at CERN 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 nonsupersymmetric 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.