  Supersymmetric (SUSY) transformations of the multi-channel Schr\"odinger
equation with equal thresholds and arbitrary partial waves in all channels are
studied. The structures of the transformation function and the superpotential
are analyzed. Relations between Jost and scattering matrices of superpartner
potentials are obtained. In particular, we show that a special type of SUSY
transformation allows us to introduce a coupling between scattering channels
starting from a potential with an uncoupled scattering matrix. The possibility
for this coupling to be trivial is discussed. We show that the transformation
introduces bound and virtual states with a definite degeneracy at the
factorization energy. A detailed study of the potential and scattering matrices
is given for the $2\times 2$ case. The possibility of inverting coupled-channel
scattering data by such a SUSY transformation is demonstrated by several
examples ($s-s$, $s-p$ and $s-d$ partial waves).
