Export Object with varying Textures

Hey Everyone,

I ran into a little problem recently when I tried to export Geometries I texured in Rhino. When I assign individual textures to the faces of the object, the Export only saves the base texture of the Object. Does anyone know a way to have the faces be exportet with the assigned textures. I tried to export as fbx and obj both failed.

Before Export:

Imported Cube with lost Textures: