It is generally assumed that structure building processes in the spoken and written modalities are subserved by modality-independent lexical, morphological, grammatical, and conceptual processes. We present a large-scale neuroimaging study (N=204) on whether the unification of sentence structure is supramodal in this sense, testing if observations replicate across written and spoken sentence materials. The activity in the unification network should increase when it is presented with a challenging sentence structure, irrespective of the input modality. We build on the well-established findings that multiple non-local dependencies, overlapping in time, are challenging and that language users disprefer left- over right-branching sentence structures in written and spoken language, at least in the context of mainly right-branching languages such as English and Dutch. We thus focused our study with Dutch participants on a left-branching processing complexity measure. Supramodal effects of left-branching complexity were observed in a left-lateralized perisylvian network. The left inferior frontal gyrus (LIFG) and the left posterior middle temporal gyrus (LpMTG) were most clearly associated with left-branching processing complexity. The left anterior middle temporal gyrus (LaMTG) and left inferior parietal lobe (LIPL) were also significant, although less specifically. The LaMTG was increasingly active also for sentences with increasing right-branching processing complexity. A direct comparison between left- and right-branching processing complexity yielded activity in an LIFG ROI for left > right-branching complexity, while the right > left contrast showed no activation. Using a linear contrast testing for increases in the left-branching complexity effect over the sentence, we found significant activity in LIFG and LpMTG. In other words, the activity in these regions increased from sentence onset to end, in parallel with the increase of the left-branching complexity measure. No similar increase was observed in LIPL. Thus, the observed functional segregation during sentence processing of LaMTG and LIPL vs. LIFG and LpMTG is consistent with our observation of differential activation changes in sensitivity to left- vs. right-branching structure. While LIFG, LpMTG, LaMTG and LIPL all contribute to the supramodal unification processes, the results suggest that these regions differ in their respective contributions to the subprocesses of unification. Our results speak to the high processing costs of (1) simultaneous unification and (2) maintenance of constituents that are not yet attached to the already unified part of the sentence. Sentences with high left- (compared to right-) branching complexity impose an added load on unification. We show that this added load leads to an increased BOLD response in left perisylvian regions. The results are relevant for understanding the neural underpinnings of the processing difficulty linked to multiple, overlapping non-local dependencies. In conclusion, we used the left- and right branching complexity measures to index this processing difficulty and showed that the unification network operates with similar spatiotemporal dynamics over the course of the sentence, during unification of both written and spoken sentences.