We present MATE, a new model for developing communication-tolerant scientific applications. MATE employs a combination of mechanisms to reduce or hide the cost of network and intra-node communication. While previous approaches have been proposed to either source of communication overhead separately, the contribution of MATE is demonstrating the symbiotic effect of reducing both forms of data movement taken together in a single unified model. We explain the rationale behind our model and show its effectiveness in three scientific computing motifs on up to 64k cores of the NERSC Cori supercomputer. Lastly, we show how MATE can improve the workload balance of an irregular multigrid solver.