Set and multiset variables are important modelling constructs in constraint programming. Several representations have been proposed for set and multiset variables, often based on combining together different representations. In this paper, we provide a formal framework with which we can study many existing combinations of representations and compare their strength. In addition, our framework opens the door to interesting new combinations, as well as to the construction of propagators with well defined properties. We illustrate the value of the framework via both theoretical and experimental results.