In the standard ``single-object'''' model of shared-memory computing, it is assumed that a process accesses at most one shared object in each of its steps. In this paper, we consider a more powerful variant---the ``multi-object'''' model---in which each process may access *any* finite number of shared objects atomically in each of its steps. We present results that relate the synchronization power of a type in the multi-object model to its synchronization power in the single-object model. Although the types fetcha all higher level types have the same unbounded synchronization power in the multi-object model stated above. This paper identifies all possible relationships between a type''s synchronization power in the single-object model and its synchronization power in the multi-object model.