We study the high-energy asymptotics of the free-channel-free-channel scattering matrix for the generalized N-body Schrodinger operator P=- Delta + Sigma _{a in A}V_a(X^a) with short-range interactions and prove that all the interactions V_a are uniquely determined by the free-channel-free-channel scattering matrix at high energies. The potentials treated are more general than the sums of pair potentials, and in fact include all possible k-particle interactions with 2<or=k<or=N.