How we combine minimal linguistic units into larger structures remains an unresolved topic in neuroscience. Language processing involves the abstract construction of ‘vertical’ and ‘horizontal’ information simultaneously (e.g., phrase structure, morphological agreement), but previous paradigms have been constrained in isolating only one type of composition and have utilized poor spatiotemporal resolution. Using intracranial recordings, we report multiple experiments designed to separate phrase structure from morphosyntactic agreement. Epilepsy patients (n = 10) were presented with auditory two-word phrases grouped into pseudoword-verb (‘trab run’) and pronoun-verb either with or without Person agreement (‘they run’ vs. ‘they runs’). Phrase composition and Person violations both resulted in significant increases in broadband high gamma activity approximately 300ms after verb onset in posterior middle temporal gyrus (pMTG) and posterior superior temporal sulcus (pSTS), followed by inferior frontal cortex (IFC) at 500ms. While sites sensitive to only morphosyntactic violations were distributed, those sensitive to both composition types were generally confined to pSTS/pMTG and IFC. These results indicate that posterior temporal cortex shows the earliest sensitivity for hierarchical linguistic structure across multiple dimensions, providing neural resources for distinct windows of composition. This region is comprised of sparsely interwoven heterogeneous constituents that afford cortical search spaces for dissociable syntactic relations.