When a set of objects is shared among several applications, multiple implementations for the set are required in order to suit each application as much as possible. Furthermore, if a set of objects could have multiple implementations, the following issues arise: (1) how to select the best implementation when processing queries on the set, and (2) how to propagate updates on an implementation of the set to the others. In this paper we propose a mechanism of multiple implementations for a set, and also give a solution for the latter issue. In the proposal a set can be of multiple types, and each of the types corresponds to an implementation already contained within the set. Update propagation can be achieved by a rewriting technique at compilation time. We also present a performance study in which the feasibility and effectiveness of our proposal were examined.