  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.
