How are systems supporting high-level cognition organized in the human brain? We hypothesize that cognitive processes involved in understanding people and places are implemented by distinct neural systems with parallel anatomical organization. We test this hypothesis using precision neuroimaging of individual human brains on diverse tasks involving perception and cognition in the domains of familiar people, places, and objects. We find that thinking about people and places elicits responses in distinct areas of high-level association cortex within the default mode network, spanning the frontal, parietal, and temporal lobes. Person- and place-preferring brain regions are systematically spatially adjacent across cortical zones. These areas have strongly domain-specific response profiles across visual, semantic, and episodic tasks and are specifically functionally connected to other parts of association cortex with like domain preference. Social and spatial networks remain anatomically separated at the apex of a unimodal-to-transmodal gradient across cortex and include regions with anatomical connections to the hippocampal formation. These results demonstrate the existence of parallel, domain-specific networks reaching the cortical apex.