Conventional diffusion-weighted MR imaging techniques provide limited specificity in disentangling disease-related microstructural alterations involving changes in both axonal density and myelination. By simultaneously probing multiple diffusion regimens, multi-shell diffusion MRI is capable of increasing specificity to different tissue sub-compartments and hence separate different contributions to changes in diffusion-weighted signal attenuation. Advanced multi-shell diffusion models impose significant requirements on the amount of diffusion weighting (i.e. gradient coil performance) and angular resolution (i.e. in-scanner subject time), which commonly limits their applicability in a clinical setting. In this paper, we apply a high-b-value, high angular resolution multi-shell diffusion MRI protocol to a population of early multiple sclerosis (MS) patients and healthy controls. Through the Composite Hindered and Restricted Model of Diffusion (CHARMED) model, we extract indices for axonal density as well as parameters sensitive to myelin. We demonstrate increased sensitivity to microstructural changes in normal appearing white matter and in lesions in MS as compared to traditional models like DTI. These changes appear to be predominantly in axonal density, pointing towards the existence of axonal damage mechanisms in early MS.