Complex cognition is dynamic, with each stage of a task requiring new cognitive processes appropriately linked to stimulus or other content. To investigate control over successive task stages, we recorded neural activity in lateral frontal and parietal cortex as monkeys carried out a complex object selection task, with each trial separated into phases of visual selection and learning from feedback. To study capacity limitation, complexity was manipulated by varying the number of object targets to be learned in each problem. Different task phases were associated with quasi-independent patterns of activity and information coding, with no suggestion of sustained activity linked to a current target. Object and location coding were largely parallel in frontal and inferior parietal cortex, though frontal cortex showed somewhat stronger object representation at feedback, and more sustained location coding at choice. At both feedback and choice, coding precision diminished as task complexity increased, matching a decline in performance. We suggest that, across successive task steps, there is radical but capacity-limited reorganization of frontoparietal activity, selecting different cognitive operations linked to their current targets.