The emergence of a variety of graph-based meaning representations (MRs) has sparked an important conversation about how to adequately represent semantic structure. MRs exhibit structural differences that reflect different theoretical and design considerations, presenting challenges to uniform linguistic analysis and cross-framework semantic parsing. Here, we ask the question of which design differences between MRs are meaningful and semantically-rooted, and which are superficial. We present a methodology for normalizing discrepancies between MRs at the compositional level (Lindemann et al., 2019), finding that we can normalize the majority of divergent phenomena using linguistically-grounded rules. Our work significantly increases the match in compositional structure between MRs and improves multi-task learning (MTL) in a low-resource setting, serving as a proof of concept for future broad-scale cross-MR normalization.