  We investigate the effect of oxygen-oxygen hopping on the three-band
copper-oxide model relevant to high-$T_c$ cuprates, finding that the physics is
changed only slightly as the oxygen-oxygen hopping is varied. The location of
the metal-insulator phase boundary in the plane of interaction strength and
charge transfer energy shifts by $\sim 0.5$eV or less along the charge transfer
axis, the quasiparticle weight has approximately the same magnitude and doping
dependence and the qualitative characteristics of the electron-doped and
hole-doped sides of the phase diagram do not change. The results confirm the
identification of La$_2$CuO$_4$ as a material with intermediate correlation
strength. However, the magnetic phase boundary as well as higher-energy
features of the optical spectrum are found to depend on the magnitude of the
oxygen-oxygen hopping. We compare our results to previously published one-band
and three-band model calculations.
