The question came in my mind because of the definition of doping. For p-type we create holes just above the valence band. This creates holes in the valence band which can contribute to conduction.
For N-type, you create electrons just beneath the conduction band, this pushes extra electrons into the conduction band which can contribute to conduction.
So, essentially, if it is chemical and material wise possible, you could also add these extra electrons or holes to an insulator?