Transition-metal dichalcogenides (TMDs), such as molybdenum disulfide (MoS2), are of significant current interest as inexpensive, earth-abundant catalysts for reactions such as electrochemical hydrogen evolution and CO2 reduction. While several high-throughput studies have focused on understanding the relative activities of various TMDs, including their multiple phases, the role of support effects on modulating adsorbate-TMD interactions is less well studied. Here, focusing on MoS2 as a model TMD, we employ density functional theory calculations to understand the interactions of monolayers of 2H, 1T, and 1T′ phases of MoS2 with three transition-metal (TM) supports: Au, Ag, and Cu. In particular, we study the interfacial energetics and charge-transfer interactions at monolayer MoS2/TM interfaces, and we correlate these with the energetic stabilization of the metastable 1T and T′ phases. We also examine the role of Cu supports in modulating the interaction of the supported monolayers with adsorbates such as H and CO, whose adsorption free energies can be considered as descriptors for hydrogen evolution and CO2 reduction reactions. While pristine basal planes of MoS2 are relatively unaffected by supports, vacancy defects, well-known active sites in the MoS2 basal plane, can be profoundly affected to the extent that catalyst poisoning becomes a distinct possibility. Our studies demonstrate that support effects ought to be taken into consideration when screening 2D TMD catalysts, especially in the presence of strong charge-transfer interactions as might be expected at interfaces between electrodes and TMD catalysts.