This study will evaluate the magnetic resonance imaging (MRI) efficacy and will investigate the safety of ofatumumab using a subcutaneous (SQ) formulation in subjects with RRMS. This Phase II study will be a multi-center, randomized, double-blind, placebo-controlled, dose ranging study in subjects with RRMS. Randomization will be stratified based on the absence or presence of GdE brain lesions present at screening. The core 54 week period of the study is made up of an up to 6-week Screening Phase, a 24-week Treatment Phase, and a 24-week Follow-up Phase. Subjects will attend the clinic a total of approximately twelve times (including Screening) during this core 54-week period of the study. Subjects who have remained enrolled and participate in the study from Screening though the end of the 24-Week Follow-Up Period (Week 48 Visit) will be considered completers. Upon completion or withdrawal from the core study period, subjects will be followed in the Individualized Follow-up Phase. Subjects will return to the clinic every 12 weeks for a B-cell count and other safety assessments. Subjects will remain in Individualized Follow-up (IFU) until CD19+ B-lymphocyte counts recover to LLN or baseline (if <LLN);OR if B-cell counts have not recovered by the Week 120 visit (100 weeks after the last possible treatment dose at Week 20), until either the B-cell counts or circulating IgG are >LLN or baseline levels (if <LLN). Male and female subjects with a diagnosis of RRMS will be screened for eligibility for the study. All non-MRI screening procedures should generally be completed within 14 days of informed consent being given. To the extent possible, investigators are to verify subjects meet all non MRI-related entry criteria before performing screening MRIs. Subjects who meet all inclusion and exclusion criteria will be centrally randomized into the study at the Baseline Visit (Week 0) to receive one of the following treatment arms: SQ administration of ofatumumab 3 mg, 30 mg, or 60 mg every 12 weeks, 60 mg every 4 weeks, or placebo. Half of the subjects randomized to the 30 mg group, or to either of the 60 mg groups, will receive a 3 mg conditioning dose at Week 0. Based on tolerability observed in other indications, the 3 mg conditioning dose may produce a more gradual lysis of B-cells, thereby reducing the cytokine release reactions to the initial 30 mg or 60 mg dose and potentially improve tolerability for subjects. The Treatment Phase lasts for 24 weeks and the subject will be seen 8 times during this phase. Upon completion or discontinuation of the Treatment Phase, subjects will enter a 24-week Follow-up Phase, during which they will not receive investigational product. Ideally, no other MS disease-modifying therapies should be taken during this period in order to allow for a clean analysis of safety data and the potential for Cluster of Differentiation (CD)+19 B-lymphocyte cell and immunoglobulin normalization to be assessed. However, if the start of a MS disease-modifying therapy is considered medically necessary, follow up will continue through the completion of the 24-Week Follow-up Phase. The subject will then be withdrawn from the study, and will not enter into the Individualized Follow-up Phase. Upon completion of the 24-Week Follow-up Phase, all subjects who have not started an MS disease modifying therapy (DMT) will enter the Individualized Follow up. During this Phase, subjects will return to the clinic every 12 weeks for a B-cell count and other safety assessments. If a subject starts a MS DMT during this follow-up phase they will be withdrawn from the study. To the extent possible, subjects experiencing a relapse during the study should return immediately to the clinic for evaluation. All MRI scans will be sent to a central reader for analysis. An Independent Data Monitoring Committee (IDMC) will evaluate risks relative to benefits through review of safety and efficacy information on an ongoing basis during the study. Approximately 245 subjects will be screened to provide around 196 subjects for randomization into the study. Assuming an attrition rate of 10% between the baseline visit and the six-month treatment visit, this will provide approximately 176 evaluable subjects.