  Two different approaches are formulated to analyze two-dimensional quantum
models which are not amenable to standard separation of variables. Both methods
are essentially based on supersymmetrical second order intertwining relations
and shape invariance - two main ingredients of the supersymmetrical quantum
mechanics. The first method explores the opportunity to separate variables in
the supercharge, and it allows to find a part of spectrum of the Schr\"odinger
Hamiltonian. The second method works when the standard separation of variables
procedure can be applied for one of the partner Hamiltonians. Then the spectrum
and wave functions of the second partner can be found. Both methods are
illustrated by the example of two-dimensional generalization of Morse potential
for different values of parameters.
