Shared object Distributed Shared Memory (DSM) minimizes the problem of false sharing by allowing programmer to control the sharing size. This shared object approach for distributed parallel programming works well in task parallelism but not in data parallelism. When the data of a shared object is being modified, a lock on that object must be enforced to exclude any concurrent access on that same object. If the shared data within an object is large, internal false sharing would become a problem. We present a multi-locking mechanism for shared object DSM which allows multiple locks be applied to the different data sets of a shared object and thus enhances its concurrency power.