Graphene exhibits unusual electronic properties, caused by a linear band structure near the Dirac point. This band structure is determined by the stacking sequence in graphene multilayers. Here we present a novel method of microscopically controlling the band structure. This is achieved by epitaxy of graphene on 3C-SiC(111) and 3C-SiC(100) thin films grown on a 3D microfabricated Si(100) substrate (3D-GOS (graphene on silicon)) by anisotropic etching, which produces Si(111) microfacets as well as major Si(100) microterraces. We show that tuning of the interface between the graphene and the 3C-SiC microfacets enables microscopic control of stacking and ultimately of the band structure of 3D-GOS, which is typified by the selective emergence of semiconducting and metallic behaviours on the (111) and (100) portions, respectively. The use of 3D-GOS is thus effective in microscopically unlocking various potentials of graphene depending on the application target, such as electronic or photonic devices.