The current trend in clusters leads towards an increase of the number of cores per node. As a result, an increasing number of parallel applications is mixing message passing and multithreading as an attempt to better match the underlying architecture's structure. This naturally raises the problem of designing efficient, multithreaded implementations of MPI. In this paper, we present the design of a multithreaded communication engine able to exploit idle cores to speed up communications in two ways: it can move CPU-intensive operations out of the critical path (e.g. PIO transfers offload), and is able to let rendezvous transfers progress asynchronously. We have implemented these methods in the PM2 software suite, evaluated their behavior in typical cases, and we have observed good performance results in overlapping communication and computation.