The primary purpose of this phase 3b study is to assess the efficacy of a modified regimen of ublituximab in participants with relapsing multiple sclerosis (RMS) as measured by T1 Gadolinium (Gd)-enhancing lesions in Part A; PK in Part B along with efficacy of ublituximab as measured by T1 Gd-enhancing lesions in participants who had a suboptimal experience on prior anti-CD20 therapy in Part C. The study consists of 3 parts: Part A is single-armed and open-label, Part B is randomized, double-blind, placebo-controlled, and Part C is single-armed and open-label.