Disruptions to brain networks, measured using either structural (sMRI), diffusion (dMRI), or resting-state functional (rs-fMRI) MRI, have been shown in people with multiple sclerosis (PwMS), highlighting the importance of damage to regions in the core of the connectome. Here, using a multilayer network approach, we aimed to integrate these three modalities to portray an enriched representation of the brain core-periphery organization and explore its alterations in PwMS. In this retrospective cross-sectional study, 1048 PwMS (695F, mean-SD age: 43.3-11.4yr), and 436 healthy controls (250F, mean-SD age: 38.3-11.8yr) with complete multimodal brain MRI acquisitions were selected from 13 European centres within the MAGNIMS network. Clinical variables included the Expanded Disability Status Scale (EDSS) and the Symbol Digit Modalities Test (SDMT), measuring physical disability and cognition, respectively. SMRI, dMRI, and rs-fMRI data were parcellated into 100 cortical (Schaefer atlas) and 14 subcortical (FSL-FIRST) regions to obtain networks of morphological covariance, structural connectivity, and functional connectivity, respectively. Following statistical harmonization and preprocessing, connectivity matrices were merged in a multiplex, from which regional coreness, defined as the probability of a node being part of the multiplex core, and coreness disruption index (kappa), quantifying the global weakening of the core-periphery structure, were computed. The associations of regional coreness and kappa with disease status (PwMS versus healthy controls), clinical phenotype, and physical (EDSS) and cognitive (SDMT z-scores) disability were tested with permutation testing, one-way ANOVA, and Spearman and Pearson correlation, respectively. We used random forest permutation feature importance to assess the relative weights of kappa in the multiplex and single-layer domains, in addition to conventional MRI measures (brain and lesion volumes), for the prediction of disease status, level of physical disability (EDSS≥4 vs EDSS<4), and cognitive impairment (SDMT z-score<-1.5). PwMS showed widespread deviations in regional coreness compared to healthy controls, with a prominent decrease in the thalami (Hedges g>0.90). At the global level, PwMS showed significant disruption of the multiplex core-periphery organization (kappa=-0.19, Hedges g=0.61, p<0.001), correlating with clinical phenotype (F=5.42, p=0.001), EDSS (rho=-0.08, p=0.01) and SDMT (r=0.19, p<0.0001). Multiplex kappa; was the only connectomic measure adding to conventional MRI for the prediction of disease status and cognitive impairment, while physical disability depended also on single-layer contributions. We show that multilayer networks represent a biologically and clinically meaningful framework to model multimodal MRI data, with disruption of the core-periphery structure emerging as a potential novel biomarker for disease severity and cognitive impairment in multiple sclerosis.