The Korringa-Kohn-Rostoker (KKR) method, a multiple scattering theory (MST) approach within density functional theory (DFT), traditionally relies on the simplifying assumption of spherically symmetric atomic potentials (muffin-tin approximation). Full-potential extensions, which account for anisotropy and charge modulation beyond the muffin-tin sphere, introduce numerical challenges, particularly in the calculation of the single-site irregular wavefunction. This presentation discusses a novel full-potential KKR implementation within the open-source MuST (https://github.com/mstsuite/MuST/) all-electron DFT code that circumvents the explicit evaluation of this wavefunction. The accuracy of this implementation is demonstrated through comparisons of total energies and forces, as well as through phonon spectrum calculations performed using the PHONOPY package with forces obtained from MuST. Furthermore, we present a full-potential scheme for core-state calculations, which is expected to significantly improve the accuracy of ab initio simulations for specific spectroscopic measurements.