  In this paper we ivestigate St\"ackel transforms between different classes of
parameter-dependent St\"ackel separable systems of the same dimension. We show
that the set of all St\"ackel systems of the same dimension splits to
equivalence classes so that all members within the same class can be connected
by a single St\"ackel transform. We also give an explicit formula relating
solutions of two St\"ackel-related systems. These results show in particular
that any two geodesic St\"ackel systems are St\"ackel equivalent in the sense
that it is possible to transform one into another by a single St\"ackel
transform. We also simplify proofs of some known statements about
multiparameter St\"ackel transform.
