An inversion algorithm based on first-order functional sensitivity analysis and Tikhonov regularization is extended for the determination of multiple (diabatic) potentials from elastic and/or inelastic scattering data. Two methods of inversion are presented. In order to illustrate the methods, two-state and three-state models of the He++Ne system are employed in a simulated inversion, the former for the recovery of an entire potential matrix, and the latter to obtain multiple coupling elements, as well as to compare and contrast the two methods against each other. In the case of the two-state model, good agreement between the recovered and the model potentials is achieved if initial guesses for V-11(r) and [V-22(r)- V-22(infinity)] are within +/-5% of the model, and those for the coupling element V-12(r) are within +/-10%, thus indicating that the method may be useful for the simultaneous refining of ab initio calculations and the determination of coupling potentials. For the three-state case, initial guesses differing from the model coupling potentials by as much as +/-50% yield successful inversions using either method, therefore indicating that the procedure may be even more useful for the recovery of multiple coupling potentials.