With the growing number of cores and fast network like Infiniband, one of the keys to performance improvement in MPI applications is the ability to overlap CPU-bound computation with network communications. While this can be done manually, this is often a complex and error prone procedure. We propose an approach that allows MPI blocking communication to act as nonblocking communication until data are needed, increasing the potential for communication and computation overlapping. Our approach, COMMMAMA, uses a separate communication thread to which communications are offloaded and a memory protection mechanism to track memory accesses in communication buffers. This guarantees both progress for these communications and the largest window during which communication and computation can be processed in parallel. This approach also significantly reduces the hassle for programmers to design MPI applications as it reduces the need to forecast when nonblocking communication should be waited.