New kinds of applications with lots of threads or irregular communication patterns which rely a lot on point-to-point MPI communications have emerged. It stresses the MPI library with potentially a lot of simultaneous MPI requests for sending and receiving at the same time. To deal with large numbers of simultaneous requests, the bottleneck lies in two main mechanisms: the tag-matching (the algorithm that matches an incoming packet with a posted receive request), and the progression engine. In this paper, we propose algorithms and implementations that overcome these issues so as to scale up to thousands of requests if needed. In particular our algorithms are able to perform constant-time tag-matching even with any-source and any-tag support. We have implemented these mechanisms in our New-Madeleine communication library. Through micro-benchmarks and computation kernel benchmarks, we demonstrate that our MPI library exhibits better performance than state-of-the-art MPI implementations in cases with many simultaneous requests.