Psychiatric disorders have been traditionally conceptualized as latent conditions producing observable symptoms, but recent studies suggest that psychopathology may emerge from symptoms interactions. Psychometric networking model these relations focusing on pairwise associations but overlooks higher-order dependencies arising among groups of variables. These dependencies may reflect synergistic mechanisms, where joint symptom configurations convey more information than pairwise relations, or redundancy, where information overlaps. We introduce an information-theoretic multiplex hypergraph framework to identify and compare higher-order interactions in eating disorders data, across diagnostic groups (e.g., anorexia nervosa). Higher-order structures are quantified using $Ω$-information, a measure that captures the balance between redundancy and synergy. To address the combinatorial growth of candidate subsets, multiple testing and estimation instability, we propose a structured pipeline comprising: (i) targeted candidate selection based on dyadic network topology and theory-driven subscale information; (ii) a three-stage inferential procedure combining null-model testing with bootstrap robustness assessment; and (iii) the construction and analysis of diagnosis-layered, synergistic and redundant multiplex hypergraphs. Results highlight how synergy captures the emergent, higher-order organization of diagnoses, revealing both a stable transdiagnostic core and diagnosis-specific ways in which these domains combine. By contrast, redundancy is confined to eating and body-image related content, marking reinforcement rather than broader symptom integration.