  In this paper we discuss maximal superintegrability of both classical and
quantum St\"ackel systems. We prove a sufficient condition for a flat or
constant curvature St\"ackel system to be maximally superintegrable. Further,
we prove a sufficient condition for a St\"ackel transform to preserve maximal
superintegrability and we apply this condition to our class of St\"ackel
systems, which yields new maximally superintegrable systems as conformal
deformations of the original systems. Further, we demonstrate how to perform
the procedure of minimal quantization to considered systems in order to produce
quantum superintegrable and quantum separable systems.
