Phase 1/2 Study to Evaluate the Safety and Efficacy of ATA188 in Subjects With Progressive Multiple Sclerosis

Inclusion Criteria: * For Part 1: History of progressive forms of MS (PPMS or SPMS), as defined by the 2010 Revised McDonald criteria for the diagnosis of MS * For Part 1: 18 to \< 66 years of age * For Part 1: EDSS scores of 3.0 to 7.0. Participants with EDSS scores of 6.5 to 7.0 must retain measurable upper limb function as assessed by the 9-hole Peg Test (9HPT). * For Part 2: Current diagnosis of a progressive form of MS (PPMS or SPMS) as defined by the 2017 Revised McDonald criteria * For Part 2:18 to \< 61 years of age * For Part 2:EDSS scores of 3.0 to 6.5 * Positive EBV serology * Willing and able to provide written informed consent Exclusion Criteria: * Clinical relapse as follows: For Part 1: Active clinical relapse between providing informed consent and the first dose of study drug. For Part 2: Documented clinical and/or radiological relapse for 2 years prior to screening, including gadolinium (Gd)-enhancing lesion(s) on any brain MRI scans available during this period (A participant will also be considered ineligible if any clinical and/or radiological relapse is reported between screening and the first dose of study drug.) * Concurrent serious uncontrolled or unresolved medical condition, such as infection, limiting protocol compliance or exposing the subject to unacceptable risk * Positive serology and/or nucleic acid testing (NAT) for human immunodeficiency virus (HIV), active hepatitis B virus (HBV) infection or carrier status for HBV, active hepatitis C vir…