The uncoupled-phase method is a nonperturbative formalism which describes the influence of any given (nth) channel on the dynamics of an n-channel scattering reaction. The method relates scattering amplitudes for the uncoupled reaction, obtained by switching off interactions to the nth channel while the interactions among the rest remain unchanged, to the scattering amplitudes describing the full reaction. We extend the uncoupled-phase method further, under exactly the same assumptions used to derive the previous uncoupled phase relations. We remove the restriction that there is only one perturbing channel and allow for the possibility of an arbitrary number of perturbing channels. The more general set of uncoupled-phase relations reduces to the previous uncoupled-phase relations when the number of perturbing channels is equal to 1. Some elementary applications of these relations is made, and their possible application in elementary particle reactions is indicated.