An extension of a recent diabatisation scheme for use in direct-dynamics variational multi-configuration Gaussian (DD-vMCG) quantum dynamics calculations is presented which allows the treatment of systems with more than two electronic states. Methodological updates to the DD-vMCG implementation are presented along with applications of the method to 2-, 3-and 4-state models of the butatriene cation. As a demonstration of the utility of the method, results of 3-state, full-dimensional calculations on the DNA base, thymine, are included, showing the energy dissipation through wavefunction population transfer between states. (C) 2017 Elsevier B.V. All rights reserved.