The traditional Distributed Shared Memory (DSM) model provides atomicity at levels of read and write on single objects. Therefore, multi-object operations such as double compare and swap, and atomic m-register assignment cannot be efficiently expressed in this model. We extend  the traditional DSM model to allow operations to span multiple objects. We show that memory consistency conditions such as sequential consistency and linearizability can be extended to this general model. We also provide algorithms to implement these consistency conditions in a distributed system.