We report an efficient extension of supercontinuum generation through dispersion engineering of crystalline aluminum nitride (AlN)-on-sapphire waveguides. Using a tailored epitaxial regrowth of AlN epilayers and an optimized fabrication protocol, the dispersion sensitivity to the waveguide cross-section was enhanced allowing for a significant reach extension of both short and long dispersive wave with optimized pumping conditions, reaching down to 550 nm in the visible and up to 4.5 mu m in the mid-infrared. (c) 2025 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.