We report an extension of the bi-epitaxial Josephson junction process that permits the use of a variety of substrate materials and allows junctions to be placed at any level of a multilayer structure. The new materials, SrTiO 3, MgO, and CeO2, serve as a base layer, a seed layer, and a buffer layer, respectively, and replace Al2O3, MgO, and SrTiO3 in the original bi-epitaxial process. This new process offers much more flexibility in designing a circuit. Bi-epitaxial junctions made with the new set of materials show much improved electrical properties, especially at 77 K. We attribute the improved electrical characteristics to a better thermal expansion match between the substrate and the thin-film layers. Important junction properties such as critical currents and junction resistances are compared to other types of grain boundary junctions.