Multichannel generalization of eigen-phase preserving supersymmetric transformations

We generalize eigen-phase preserving (EPP) supersymmetric (SUSY) transformations to $N>2$ channel Schr\"odinger equation with equal thresholds. It is established that EPP SUSY transformations exist only in the case of even number of channels, $N=2M$. A single EPP SUSY transformation provides an $M(M-1)+2$ parametric deformation of the matrix Hamiltonian without affecting eigen-phase shifts of the scattering matrix.