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 virus (HCV) infection
* For Part 1: Positive serology for syphilis or human T cell lymphotrophic virus I/II
* Uncontrolled psychosis, uncontrolled depression or suicide risk, substance dependence, or any other psychiatric condition that may compromise the ability to participate in this trial
* Clinically significant abnormalities of full blood count, renal function, or hepatic function
* Any contraindication to MRI and/or Gd, eg., any object that is reactive to strong static magnetic, pulsed-gradient fields including any metallic fragments or foreign body (eg, aneurysm clip\[s\], pacemakers, electronic implants, shunts)
* Any history of cancer (as exceptions, successfully treated non-melanoma skin cancer or carcinoma in situ of the cervix with a \< 5% chance of recurrence within 12 months of providing informed consent are allowed.)
* Prior therapy with corticosteroids (within 2 weeks before Cycle 1 Day 1)
* Prior therapy (30 days) B-cell depleting agent (eg, anti-CD20 agents such as ocrelizumab); participant must be progressing despite therapy to be eligible
* For Part 1: Prior therapy (6 half-lives or 30 days whichever is longer) with cladribine, glatiramer acetate, interferon β, dimethyl fumarate, methotrexate, azathioprine, cyclosporine, fingolimod, natalizumab, teriflunomide, mitoxantrone, cyclophosphamide, any other immunosuppressant or cytotoxic therapy (other than steroids), antithymocyte globulin or similar anti-T-cell antibody therapy, or any other investigational product
* For Part 1: Any previous treatment with alemtuzumab, ablative stem cell transplant, or EBV T-cell therapy
* For Part 2: Prior therapy (6 half-lives or 30 days whichever is longer) with IV immunoglobin, plasmapheresis, Bruton's tyrosine kinase inhibitors, all sphingosine 1-phosphate receptor modulators (eg, fingolimod), glatiramer acetate, interferon β, nuclear factor (erythroid-derived 2)-like 2 (Nrf2) activators (eg, dimethyl fumarate), methotrexate, azathioprine, cyclosporine, natalizumab, teriflunomide, mitoxantrone, cyclophosphamide, any other immunosuppressant or cytotoxic therapy (other than steroids), antithymocyte globulin or similar anti-T-cell antibody therapy, or any other investigational product
* For Part 2: Any previous treatment with cladribine, alemtuzumab, ablative stem cell transplant, or EBV T-cell therapy
* Unresolved reactions from previous therapies that may, in the investigator's opinion, impact the safety of the participant or the conduct of this study
* Unwilling to use protocol specified contraceptive methods
* Women who are breastfeeding
* Pregnancy
* Inability or unwillingness to comply with study procedures