If you know that the parts names (e.g. material names in the OBJ) will be the same for all objects, you can point all object to the same Parts Shader. You could copy that Parts Shader to the root of the network and I think it should still work.
In situations like this, you can avoid spending lots of time in context menus by remembering that node connections are simply text that you can copy from one properties window to another. So you might put your Parts Shader in the root of the network, and paste "/Parts shader 01" into the Surface Shader field of the object.
Connecting to a shader outside of the object might prevent you from saving the whole package as a TGO, if that's important to you.