  Using the disconjugacy properties of the Schr\"odinger equation, it is
possible to develop a new type of generalized SUSY QM partnership which allows
to generate new solvable rational extensions for translationally shape
invariant potentials having a finite bound state spectrum. For this we prolong
the dispersion relation relating the energy to the quantum number out of the
physical domain until a disconjugacy sector. The prolonged excited states
Riccati-Schr\"odinger (RS) functions are used to build Darboux-B\"acklund
transforms which give regular isospectral extensions of the initial potential.
We give the spectra of these extensions in terms of new orthogonal polynomials
and study their shape invariance properties.
