A facility is provided for communicating among processes in a symmetric multi-processing (SMP) cluster environment wherein at least some SMP nodes of the SMP cluster include multiple processes. The facility includes transferring intra-nodal at an SMP node messages of a collective communication among processes employing a shared memory of the SMP node; and responsive to the intra-nodal transferring, concurrently transferring inter-nodal multiple messages of the collective communication from n SMP node(s) to m other SMP node(s), wherein at least one of n or m is greater than one. The concurrently transferring is performed by multiple processes of at least one of the n SMP node(s) or the m other SMP node(s). More particularly, the facility includes concurrently transferring inter-nodal the multiple messages from one of: one SMP node to multiple other SMP nodes, multiple SMP nodes to one other SMP node, or multiple SMP nodes to multiple other SMP nodes.