Generalized symplectic symmetric spaces

Bielavsky introduced and investigated the class of symmetric symplectic spaces, that is, symmetric spaces endowed with a symplectic form invariant with respect to symmetries. Since the theory of symmetric spaces has generalizations, we ask a question about their possible symplectic versions. We do construct such generalizations and extend some of Bieliavsky's results. In particular, we classify all 3-symmetric symplectic spaces.