Stackel transform of Lax equations

We construct a map between Lax equations for pairs of Liouville integrable Hamiltonian systems related by a multiparameter Stackel transform. Using this map, we construct Lax representation for a wide class of separable systems by applying the multiparameter Stackel transform to Lax equations of suitably chosen systems from a seed class. For a given separable system, we obtain in this way a set of nonequivalent Lax equations parameterized by an arbitrary function of the spectral parameter, as it is in the case of a related seed system