  A method to construct trihamiltonian extensions of a separable system is
presented. The procedure is tested for systems, with a natural Hamiltonian,
separable in classical sense in one of the four orthogonal separable coordinate
systems of the Euclidean plane, and some explicit examples are constructed.
Finally a conjecture on possible generalizations to other classes of systems is
discussed: in particular, the method can be easily adapted to the eleven
orthogonal separable coordinate sets of the Euclidean three-space.
