We investigate media which exhibits epsilon-near-zero (ENZ) behavior while simultaneously sustaining stopped light energy bands which contain multiple points of zero group velocity (ZGV). This allows the merging of state-of-the-art phenomena that was hitherto attainable in media that demonstrated these traits separately. Specifically, we demonstrate the existence of Ferrell-Berreman (FB) modes within frequency bands bounded by points of ZGV with the goal to improve the coupling efficiency and localization of light in the media. The FB mode is formed within a double layer, thin-film stack where at subwavelength thicknesses the structure exhibits a very low reflection due to ENZ behavior. In addition, the structure is engineered to promote a flattened frequency dispersion with a negative permittivity able to induce multiple points of ZGV. For proof-of-concept, we propose an oxide-semiconductor-oxide-insulator stack and discuss the useful optical properties that arise from combining both phenomena. A transfer matrix (TM) treatment is used to derive the reflectivity profile and dispersion curves. Results show the ability to reduce reflection below 0.05% in accordance with recent experimental data while simultaneously exciting a polariton mode exhibiting both reduced group velocity and group velocity dispersion (GVD).