Starting from reliable double many-body expansion potentials calibrated with energies calculated at the state-of-the-art ab initio level but of varying accuracies, it is shown that a single scaling parameter suffices to bring them into consistency while mimicking key experimental data and leaving mostly unaffected crossing seams of the conical type. This emerges as a valuable asset of their underlying formalism. Use of the novel potentials for studying the dynamics of the N(S-4/D-2) + N-2((1)Sigma(g)+) reactions yields results in excellent agreement with the most accurate available data.