Recent research has characterized the anatomical connectivity of the cortico-cerebellar system - a large and important fibre system in the primate brain. Within this system, there are reciprocal projections between the prefrontal cortex and Crus II of the cerebellar cortex, which both play important roles in the acquisition and execution of cognitive skills. Here, we propose that this system also plays a particular role in sustaining skilled cognitive performance in patients with Relapsing-Remitting Multiple Sclerosis (RRMS), in whom advancing neuropathology causes increasingly inefficient information processing. We scanned RRMS patients and closely matched healthy subjects while they performed the Paced Auditory Serial Addition Test (PASAT), a demanding test of information processing speed, and a control task. This enabled us to localize differences between conditions that change as a function of group (group-by-condition interactions). Hemodynamic activity in some patient populations with CNS pathology are not well understood and may be atypical, so we avoided analysis strategies that rely exclusively on models of hemodynamic activity derived from the healthy brain, using instead an approach that combined a 'model-free' analysis technique (Tensor Independent Component Analysis, TICA) that was relatively free of such assumptions, with a post-hoc 'model-based' approach (General Linear Model, GLM). Our results showed group-by-condition interactions in cerebellar cortical Crus II. We suggest that this area may have in role maintaining performance in working memory tasks by compensating for inefficient data transfer associated with white matter lesions in MS.