We propose a novel multi-component analysis for MR fingerprinting that enables detection of small lesions, while taking partial volume effects into account. The algorithm uses a joint sparsity constraint limiting the number of components in local regions. It is evaluated in simulations and on MRF-EPI data from a patient with multiple sclerosis (MS). MS-lesions are separated from other tissues based on having increased T2* relaxation times. The improved sensitivity to multiple components makes it possible to detect components with long relaxation times within the lesion, possibly increasing our insight into these small pathologies.