An epoxy–anhydride formulation used for the coating electrical devices was modified with a commercially available hyperbranched poly(ester amide), Hybrane S2200, to improve the thermal degradability of the resulting thermoset and, thus, facilitate the recovery of substrate materials after the service life of the component. The thermomechanical, mechanical, and dielectric properties and thermal degradability were studied and interpreted in terms of the composition and network structure of the cured thermosets. Although the crosslinking density was significantly reduced with the incorporation of S2200, the glass transition temperature of the fully cured material (Tg∞) of the modified thermoset was hardly affected because of the enhancement of H-bonding interactions in the presence of S2200. Despite the different network structures, the combined dielectric and dynamic mechanical analysis revealed that the relaxation dynamics of both networks were very similar. In terms of application, improvements in the dielectric and mechanical properties were observed. The incorporation of S2200 accelerated the thermal decomposition of the material and, thus, facilitated the recovery of the valuable parts from the substrate at the end of the service life of the apparatus