A Multiple Dose Study of ABT-555 in Subjects With Relapsing Forms of Multiple Sclerosis

* Currently receiving one of the following MS medications for at least 3 months: beta-interferon (any formulation including the pegylated form), glatiramer acetate (Copaxone®, others), teriflunomide (Aubagio®), fingolimod (Gilenya®), or dimethyl fumarate (Tecfidera®); OR * Has not been treated with an MS immunotherapy for the past 6 months (12 months if they previously received cyclophosphamide or alemtuzumab); OR * Treatment naïve with established MS diagnosis per criteria by a neurologist. * Diagnosis of relapsing-remitting MS (RRMS) or secondary progressive MS (SPMS) according to revised McDonald criteria * Baseline Expanded Disability Status Scale (EDSS) between 0 and 6.0, inclusive. * Brain MRI scan at Screening that did not show evidence of overt vascular lesions, masses, mass effect or other abnormalities other than those compatible with MS, which would preclude the participant from undergoing a lumbar puncture/spinal tap for CSF collection

* Diagnosis of primary progressive MS. * Anticipated maintenance immunomodulator change, either agent or dose * An MS relapse that occurred within the 30 days prior to randomization AND/OR the participant has not stabilized from a previous relapse prior to randomization * Participants for whom MRI is contraindicated * Participants who have claustrophobia that cannot be medically managed or are unable to lie still for 1 hour or more for the imaging procedures * Findings on brain MRI scan indicating any clinically significant brain abnormality other than MS * Contraindication for lumbar puncture