A distributed, frontoparietal “multiple-demand” (MD) network is involved in tasks of many different kinds. Integrated activity across this network may be needed to bind together the multiple features of a mental control program (Duncan, 2013). Previous data suggest that, especially with low cognitive load, there may be some differentiation between MD regions (e.g., anterior vs. posterior regions of lateral frontal cortex), but with increasing load, there is progressive recruitment of the entire network. Differentiation may reflect preferential access to different task features, whereas co-recruitment may reflect information exchange and integration. To examine these patterns, we used manipulations of complexity, time pressure, and reward while participants solved a spatial maze. Complexity was manipulated by combining two simple tasks. Time pressure was added by fading away the maze during route planning, and on some of these trials, there was the further possibility of a substantial reward. Simple tasks evoked activity only in posterior MD regions, including posterior lateral frontal cortex, pre-supplementary motor area/anterior cingulate, and intraparietal sulcus. With increasing complexity, time pressure, and reward, increases in activity were broadly distributed across the MD network, though with quantitative variations. Across the MD network, the results show a degree of functional differentiation, especially at low load, but strong co-recruitment with increased challenge or incentive.