A Study of Ocrelizumab in Participants With Relapsing Remitting Multiple Sclerosis (RRMS) Who Have Had a Suboptimal Response to an Adequate Course of Disease-Modifying Treatment (DMT)

This study will evaluate the efficacy and safety of ocrelizumab in participants with RRMS who have had a suboptimal response to an adequate course of DMT. Participants will receive ocrelizumab as an initial dose of two 300-milligrams (mg) intravenous (IV) infusions (600 mg total) separated by 14 days followed by one 600-mg IV infusion for a maximum of 4 doses (up to 96 weeks). Anticipated time on study treatment is 96 weeks.

Participants who complete their Week 72 ocrelizumab infusion and do not experience any serious infusion related reaction (IRR) throughout the main study will be eligible to enroll in an optional, open-label, non-randomized substudy to MN30035 and receive one additional shorter infusion of ocrelizumab at the Week 96 visit. This substudy will enroll approximately 100 patients from MN30035 main study.

Eligibility Criteria:
Inclusion Criteria:

* Diagnosis of multiple sclerosis (specifically RRMS), in accordance with the revised 2010 McDonald criteria
* Disease duration from first symptom of less than or equal to (\</=) 12 years
* Treated with an adequate course of treatment with no more than three prior DMT regimens of greater than or equal to (\>/=) 6 months, and the discontinuation of the most recent adequately used DMT was due to suboptimal response
* Suboptimal response while the participant was on his/her last adequately used DMT for \>/=6 months (defined by having one of the following qualifying events despite being on a stable dose of the same DMT for at least 6 months: one or more clinically reported relapses, one or more T1 Gd-enhanced lesions, or two or more new or enlarging T2 lesions on MRI); these qualifying events must have occurred while on the last adequately used DMT. In participants receiving stable doses of the same approved DMT for more than a year, the event must have occurred within the last 12 months of treatment with this DMT from the date of screening

Exclusion Criteria:

* History of primary progressive multiple sclerosis (PPMS), progressive relapsing multiple sclerosis (PRMS), or secondary progressive multiple sclerosis (SPMS)
* Contraindications for MRI
* Known presence of other neurological disorders that may mimic multiple sclerosis
* Pregnancy or lactation, or intention to become pregnant during the study
* Requirement for chronic treatment with systemic corticosteroids or immunosuppressants during the course of the study
* History of or currently active primary or secondary immunodeficiency
* Lack of peripheral venous access
* History of severe allergic or anaphylactic reactions to humanized or murine monoclonal antibodies
* Active infection, or history of or known presence of recurrent or chronic infection such as human immunodeficiency virus (HIV), syphilis, or tuberculosis
* History of progressive multifocal leukoencephalopathy
* Contraindications to or intolerance of oral or IV corticosteroids
* Previous treatment with fingolimod (Gilenya®) or dimethyl fumarate (Tecfidera®) in participants whose lymphocyte count is below the lower limit of normal (LLN)
* Treatment with alemtuzumab (Lemtrada®)
* Previous treatment with systemic cyclophosphamide, azathioprine, mycophenolate mofetil, cyclosporine, or methotrexate
* Previous treatment with natalizumab within 12 months prior to screening unless failure was due to confirmed, persistent anti-drug antibodies (ADAs). Participants previously treated with natalizumab will be eligible for this study only if duration of treatment with natalizumab was less than (\<) 1 year and natalizumab was not used in the 12 months prior to screening. Anti-John Cunningham virus (JCV) antibody status (positive or negative) and titer (both assessed within the year of screening) must be documented prior to enrollment
* Treatment with dalfampridine (Ampyra®) unless on stable dose for \>/=30 days prior to screening
* Treatment with a B-cell targeted therapies (e.g., rituximab, ocrelizumab, atacicept, belimumab, or ofatumumab)
* Treatment with a drug that is experimental (Exception: treatment with an experimental drug that was subsequently approved in the participant's country is allowed)