  A class of three-dimensional models which satisfy supersymmetric intertwining
relations with the simplest - oscillator-like - variant of shape invariance is
constructed. It is proved that the models are not amenable to conventional
separation of variables for the complex potentials, but their spectra are real
and equidistant (like for isotropic harmonic oscillator). The special case of
such potential with quadratic interaction is solved completely. The Hamiltonian
of the system is non-diagonalizable, and its wave functions and associated
functions are built analytically. The symmetry properties of the model and
degeneracy of energy levels are studied.
