Two parietofrontal networks share the control of goal-directed movements: a dorsomedial circuit that includes the superior parieto-occipital sulcus (sPOS) and a dorsolateral circuit comprising the anterior intraparietal sulcus (aIPS). These circuits are thought to independently control either reach and grip components (a functional dissociation), or planning and execution phases of grasping movements (a temporal dissociation). However, recent evidence of functional and temporal overlap between these circuits has undermined those models. Here, we test an alternative model that subsumes previous accounts: the dorsolateral and dorsomedial circuits operate at different hierarchical levels, resulting in functional and temporal dependencies between their computations. We asked human participants to grasp a visually presented object, manipulating movement complexity by varying object slant. We used concurrent single-pulse transcranial magnetic stimulation and electroencephalography (TMS-EEG) to probe and record neurophysiological activity in the two circuits. Changes in alpha-band oscillations (8-12 Hz) characterized the effects of task manipulations and TMS interferences over aIPS and sPOS. Increasing the complexity of the grasping movement was accompanied by alpha-suppression over dorsomedial parietofrontal regions, including sPOS, during both planning and execution stages. TMS interference over either aIPS or sPOS disrupted this index of dorsomedial computations; early when aIPS was perturbed, later when sPOS was perturbed, indicating that the dorsomedial circuit is temporally dependent on aIPS. TMS over sPOS enhanced alpha-suppression in inferior parietal cortex, indicating that the dorsolateral circuit can compensate for a transient sPOS perturbation. These findings suggest that both circuits specify the same grasping parameters, with dorsomedial computations depending on dorsolateral contributions.