Nonequilibrium effects may have a profound impact on the performance of thermal devices performing thermodynamic tasks such as refrigeration or heat pumping. The possibility of enhancing the performance of thermodynamic operations by means of quantum coherence is of particular interest but requires an adequate characterization of heat and work at the quantum level. In this work, we demonstrate that the presence of even small amounts of coherence in the thermal reservoirs powering a three-terminal machine, enables the appearance of combined, and hybrid modes of operation, where either different resources are combined to perform a single thermodynamic task, or more than one task is performed at the same time. We determine the performance of such coherence-enabled modes of operation obtaining their power and efficiency. In the case of hybrid regimes, the presence of coherence in the hot bath allows for an increase in power while maintaining high efficiencies. On the other hand, in combined regimes, a contrasting behavior emerges whereby coherence has a detrimental impact on power output and efficiency.