  Recently, a new quantum model - two-dimensional generalization of the Scarf
II - was completely solved analytically by SUSY method for the integer values
of parameter. Now, the same integrable model, but with arbitrary values of
parameter, will be studied by means of supersymmetrical intertwining relations.
The Hamiltonian does not allow the conventional separation of variables, but
the supercharge operator does allow, leading to the partial solvability of the
model. This approach, which can be called as the first variant of
SUSY-separation, together with shape invariance of the model, provides
analytical calculation of the part of spectrum and corresponding wave functions
(quasi-exact-solvability). The model is shown to obey two different variants of
shape invariance which can be combined effectively in construction of energy
levels and wave functions.
