We describe an Aldous–Hoover-type characterization of random relational structures that are exchangeable relative to a fixed structure which may have various equivalence relations. Our main theorem gives the common generalization of the results on relative exchangeability due to Ackerman \)-invariant measures: part I, 2015. arXiv:1509.06170) and Crane and Towsner and hierarchical exchangeability results due to Austin and Panchenko :809–823, 2014).