Pompe disease (PD) is a monogenic autosomal recessive disorder caused by biallelic pathogenic variants of the GAA gene encoding lysosomal alpha-glucosidase; its loss causes glycogen storage in lysosomes, mainly in the muscular tissue. The genotype–phenotype correlation has been extensively discussed, and caution is recommended when interpreting the clinical significance of any mutation in a single patient. As there is no evidence that environmental factors can modulate the phenotype, the observed clinical variability in PD suggests that genetic variants other than pathogenic GAA mutations influence the mechanisms of muscle damage/repair and the overall clinical picture. Genes encoding proteins involved in glycogen synthesis and catabolism may represent excellent candidates as phenotypic modifiers of PD. The genes analyzed for glycogen synthesis included UGP2, glycogenin (GYG1-muscle, GYG2, and other tissues), glycogen synthase (GYS1-muscle and GYS2-liver), GBE1, EPM2A, NHLRC1, GSK3A, and GSK3B. The only enzyme involved in glycogen catabolism in lysosomes is α-glucosidase, which is encoded by GAA, while two cytoplasmic enzymes, phosphorylase (PYGB-brain, PGL-liver, and PYGM-muscle) and glycogen debranching (AGL) are needed to obtain glucose 1-phosphate or free glucose. Here, we report the potentially relevant variants in genes related to glycogen synthesis and catabolism, identified by whole exome sequencing in a group of 30 patients with late-onset Pompe disease (LOPD). In our exploratory analysis, we observed a reduced number of variants in the genes expressed in muscles versus the genes expressed in other tissues, but we did not find a single variant that strongly affected the phenotype. From our work, it also appears that the current clinical scores used in LOPD do not describe muscle impairment with enough qualitative/quantitative details to correlate it with genes that, even with a slightly reduced function due to genetic variants, impact the phenotype.