Corticocortical (CC) projections in the visual system facilitate hierarchical processing of sensory information. In addition to direct CC connections, indirect cortico-thalamo-cortical (CTC) pathways through the pulvinar nucleus of the thalamus can relay sensory signals and mediate cortical interactions according to behavioral demands. While the pulvinar connects extensively to the entire visual cortex, it is unknown whether transthalamic pathways link all cortical areas or whether they follow systematic organizational rules. Because mouse pulvinar neurons projecting to different areas are spatially intermingled, their input/output relationships have been difficult to characterize using traditional anatomical methods. To determine the organization of CTC circuits, we mapped the higher visual areas (HVAs) of male and female mice with intrinsic signal imaging and targeted five pulvinar→HVA pathways for projection-specific rabies tracing. We aligned postmortem cortical tissue to in vivo maps for precise quantification of the areas and cell types projecting to each pulvinar→HVA population. Layer 5 corticothalamic (L5CT) "driver" inputs to the pulvinar originate predominantly from primary visual cortex (V1), consistent with the CC hierarchy. L5CT inputs from lateral HVAs specifically avoid driving reciprocal connections, consistent with the "no-strong-loops" hypothesis. Conversely, layer 6 corticothalamic (L6CT) "modulator" inputs are distributed across areas and are biased toward reciprocal connections. Unlike previous studies in primates, we find that every HVA receives disynaptic input from the superior colliculus. CTC circuits in the pulvinar thus depend on both target HVA and input cell type, such that driving and modulating higher-order pathways follow complementary connection rules similar to those governing first-order CT circuits.