This study investigated two questions. One is: To what degree is sentence processing beyond single words independent of the input modality (speech vs. reading)? The second question is: Which parts of the network recruited by both modalities is sensitive to syntactic complexity? These questions were investigated by having more than 200 participants read or listen to well-formed sentences or series of unconnected words. A largely left-hemisphere frontotemporoparietal network was found to be supramodal in nature, i.e., independent of input modality. In addition, the left inferior frontal gyrus (LIFG) and the left posterior middle temporal gyrus (LpMTG) were most clearly associated with left-branching complexity. The left anterior temporal lobe (LaTL) showed the greatest sensitivity to sentences that differed in right-branching complexity. Moreover, activity in LIFG and LpMTG increased from sentence onset to end, in parallel with an increase of the left-branching complexity. While LIFG, bilateral anterior temporal lobe, posterior MTG, and left inferior parietal lobe (LIPL) all contribute to the supramodal unification processes, the results suggest that these regions differ in their respective contributions to syntactic complexity related processing. The consequences of these findings for neurobiological models of language processing are discussed.