Research on the processing of objects at different hierarchical levels has suggested that understanding superordinate concepts (e.g. fruit), relative to basic level concepts (e.g. apple), requires greater semantic control demands. Yet, it is unclear which factors underlie this difference in executive processing. We built on previous research showing that superordinate concepts have less shared features among their members and therefore may involve higher semantic control requirements. To test this hypothesis, we developed an fMRI study in which we orthogonally manipulated feature sharedness (more shared vs. less shared) and concept level (superordinate vs. basic) in a sentence verification task. Sentences involving less shared features, relative to more shared features, significantly engaged the L lateral PFC. Importantly, sentences that included superordinate concepts, relative to those with basic level concepts, also revealed a stronger response in L lateral PFC, along with posterior temporal gyrus activation. There was also a significant interaction between feature sharedness and concept level in several PFC regions and L posterior temporal areas. The results suggest that relative to basic level concepts, processing superordinate concepts requires extra semantic control in L lateral PFC to coordinate information that is less shared by other members of the category level. These findings demonstrate that feature sharedness impacts the neural basis of semantic knowledge, and is a critical dimension in the processing of superordinate concepts.