  In this paper, we show that an attempt to construct shape invariant
extensions of a known shape invariant potential leads to, apart from a shift by
a constant, the well known technique of isospectral shift deformation. Using
this, we construct infinite sets of generalized potentials with $X_m$
exceptional polynomials as solutions. These potentials are rational extensions
of the existing shape invariant potentials. The method is elucidated using the
radial oscillator and the trigonometric P\"{o}schl-Teller potentials. For the
case of radial oscillator, in addition to the known rational extensions, we
construct two infinite sets of rational extensions, which seem to be less
studied. For one of the potential, we show that its solutions involve a third
type of exceptional Laguerre polynomials. Explicit expressions of this
generalized infinite set of potentials and the corresponding solutions are
presented. For the trigonometric P\"{o}schl-Teller potential, our analysis
points to the possibility of several rational extensions beyond those known in
literature.
