Study to Evaluate Safety, Efficacy and Pharmacokinetics (PK) of a Modified Regimen of Ublituximab

Inclusion Criteria: * Diagnosis of RMS (2017 Revised McDonald criteria). * Participants must meet one of the following prior treatment definitions: 1. Participants naïve to treatment. 2. Participants previously treated with a disease modifying therapy (DMT) who have discontinued treatment prior to consent and meet the washout requirements. * Expanded Disability Status Scale (EDSS) score ≤ 5.5 at screening. * Neurologically stable for \> 30 days prior to first dose of ublituximab. * Female participants of childbearing potential must consent to use a medically acceptable method of contraception from consent, throughout the study period, and for 6 months after the last dose of ublituximab. * Part C: participants currently treated with an anti-CD20 agent for at least 6 months and meet the washout requirements prior to W1D1. * Part C: Discontinuation of current anti-CD20 must be due to suboptimal experience Exclusion Criteria: * History of any serious 3 Infusion Related Reaction (IRR) on prior anti-CD20 therapy. * Primary-progressive multiple sclerosis (PPMS) or inactive Secondary Progressive MS (SPMS). * Active chronic (or stable but treated with immune therapy) disease of the immune system other than MS (e.g., rheumatoid arthritis, scleroderma, Sjögren's syndrome, Crohn's disease, ulcerative colitis, etc.) or immunodeficiency syndrome (hereditary immune deficiency, drug-induced immune deficiency, etc.). * Current evidence or known history of clinically significant infection, including: chronic, recurrent, or ongoing active viral, bacterial, or fungal infectious disease requiring long term systemic treatment such as, but not limited to chronic urinary tract infection, chronic pulmonary infection with bronchiectasis, tuberculosis, or active hepatitis C virus (HCV). * Previous serious opportunistic or atypical infection. * Evidence of chronic active or history of hepatitis B virus (HBV) infection as evidenced by a detectable hepatitis B surface antigen (HBsAg), or positive hepatitis B core antibody (HBcAb), or chronic hepatitis C infection. Participants with positive hepatitis C virus antibody (HCV Ab) are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA). * History or evidence (clinical, radiological, or biomarker) of suspected or confirmed progressive multifocal leukoencephalopathy (PML). * Receipt of any live or live-attenuated vaccines (including vaccines for varicella-zoster virus or measles) within 4 weeks prior to first study drug administration. * Participants requiring treatment with intravenous immune globulin (IVIG) for decreased immunoglobulins within the 12 months prior to W1D1. * Any active malignancies other than adequately treated basal, squamous cell or in situ carcinoma. * Participants who have ever received ublituximab, alemtuzumab, cyclophosphamide, mitoxantrone, cladribine, or daclizumab (including for non-MS indications). Note: Other Inclusion/Exclusion criteria may apply.