  We discuss a possibility whether a model of grand gauge-Higgs unification
incorporating family unification in higher dimensions can be constructed. We
first extend a five dimensional $SU(6)$ grand gauge-Higgs unification model to
a five dimensional $SU(7)$ grand gauge-Higgs unification model compactified on
an orbifold $S^1/Z_2$ to obtain three generations of quarks and leptons after
symmetrybreaking of the larger family unified gauge group. A prescription of
constructing a six dimensional $SU(N)$ grand gauge-Higgs unification model
including a five dimensional $SU(7)$ grand gauge-Higgs unification after
compactifying the sixth dimension on an orbifold $S^1/Z_2$ is given. We find a
six dimensional $SU(14)$ grand gauge-Higgs unification model with a set of
representations containing three generations of quarks and leptons.
