  In some recent articles we developed a new systematic approach to generate
solvable rational extensions of primary translationally shape invariant
potentials. In this generalized SUSY QM partnership, the DBT are built on the
excited states Riccati-Schr\"odinger (RS) functions regularized via specific
discrete symmetries of the considered potential. In the present paper, we prove
that this scheme can be extended in a multistep formulation. Applying this
scheme to the isotonic oscillator, we obtain new towers of regular rational
extensions of this potential which are strictly isospectral to it. We give
explicit expressions for their eigenstates which are associated to the recently
discovered exceptional Laguerre polynomials and show explicitely that these
extensions inherit of the shape invariance properties of the original
potential.
