  Spectral properties of a coupled $N \times N$ potential model obtained with
the help of a single non-conservative supersymmetric (SUSY) transformation
starting from a system of $N$ radial Schr\"odinger equations with the zero
potential and finite threshold differences between the channels are studied.
The structure of the system of polynomial equations which determine the zeros
of the Jost-matrix determinant is analyzed. In particular, we show that the
Jost-matrix determinant has $N2^{N-1}$ zeros which may all correspond to
virtual states. The number of bound states satisfies $0\leq n_b\leq N$. The
maximal number of resonances is $n_r=(N-1)2^{N-2}$. A perturbation technique
for a small coupling approximation is developed. A detailed study of the
inverse spectral problem is given for the $2\times 2$ case.
