The performance and degree of efficiency of industrial transformers are directly influenced by the magnetic properties of high-permeability steel laminations (HPSLs). Industrial transformer cores are built of stacks of single HPSLs. While the insulating coating on each HPSL reduces eddy-current losses in the transformer core, the coating also induces favorable inter-granular tensile stresses that significantly influence the underlying magnetic domain structure. Here, we show that the neutron dark-field image can be used to analyze the influence of the coating on the volume and supplementary surface magnetic domain structures. To visualize the stress effect of the coating on the bulk domain formation, we used an uncoated HPSL and stepwise increased the applied external tensile stress up to 20 MPa. We imaged the domain configuration of the intermediate stress states and were able to reproduce the original domain structure of the coated state. Furthermore, we were able to visualize how the applied stresses lead to a refinement of the volume domain structure and the suppression and reoccurrence of supplementary domains.