Recent cluster architectures include dozens of cores per node, with all cores sharing the network resources. To program such architectures, hybrid models mixing MPI+threads, and in particular MPI+OpenMP are gaining popularity. This imposes new requirements on communication libraries, such as the need for MPI_THREAD_MULTIPLE level of multi-threading support. Moreover, the high number of cores brings new opportunities to parallelize communication libraries, so as to have proper background progression of communication and communication/computation overlap. In this paper, we present pioman, a generic framework to be used by MPI implementations, that brings seamless asynchronous progression of communication by opportunistically using available cores. It uses system threads and thus is composable with any runtime system used for multithreading. Through various benchmarks, we demonstrate that our \texttt{pioman}-based MPI implementation exhibits very good properties regarding overlap, progression, and multithreading, and outperforms state-of-art MPI implementations.