Known multiple sclerosis (MS) susceptibility variants can only explain half of the disease’s estimated heritability, whereas low-frequency and rare variants may partly account for the missing heritability. Thus, here we sought to determine the occurrence of rare functional variants in a large Italian MS multiplex family with five affected members. For this purpose, we combined linkage analysis and next-generation sequencing (NGS)-based whole exome and whole genome sequencing (WES and WGS, respectively). The genetic burden attributable to known common MS variants was also assessed by weighted genetic risk score (wGRS). We found a significantly higher burden of common variants in the affected family members compared to that observed among sporadic MS patients and healthy controls (HCs). We also identified 34 genes containing at least one low-frequency functional variant shared among all affected family members, showing a significant enrichment in genes involved in specific biological processes—particularly mRNA transport—or neurodegenerative diseases. Altogether, our findings point to a possible pathogenic role of different low-frequency functional MS variants belonging to shared pathways. We propose that these rare variants, together with other known common MS variants, may account for the high number of affected family members within this MS multiplex family.