Abstract We study the renormalizable group equations (RGEs) of the extended strong and weak gauge couplings in an SU(8) theory, where three-generational SM fermions are non-trivially embedded. This framework was previously found to generate the observed SM quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa mixing pattern through its maximally breaking pattern. The field theoretical two-loop RGEs can not achieve the gauge coupling unification with the minimal setup, unless additional adjoint Higgs fields as well as the gravity-induced d = 5 term to the SU(8) field strength term are included.