Inclusion Criteria:

A subject will be considered eligible to participate in this study if all of the following are satisfied:

• History of MS, with progressive forms of MS or RRMS as defined by the 2010 Revised McDonald criteria for the diagnosis of MS:
  • Subjects with RRMS must have failed a health authority approved treatment.
• Positive EBV serology
• Males and females of the following ages:
  • 18 to 65 years of age for subjects with progressive forms of MS;
  • 18 to 45 years of age for subjects with RRMS.
• EDSS scores as follows:
  • 3.0 to 6.5 for subjects with progressive forms of MS;
  • 2.0 to 5.5 for subjects with RRMS.
• Willing and able to provide written informed consent.

Exclusion Criteria:

A subject will not be eligible to participate in the study if any of the following criteria are met:

• Active clinical relapse between providing informed consent and enrollment (ie, date of the first dose of ATA188)
• 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).
• Serology and/or NAT indicating active hepatitis B virus (HBV) infection or carrier status for HBV (Note: A positive serology for HBV indicating a previous but cleared infection with HBV is not an exclusion criterion).
• Serology and/or NAT indicating active hepatitis C virus (HCV) infection.
• Positive serology for syphilis or human T cell lymphotrophic virus I/II (HTLV).
• Significant non-malignant disease (eg, severe cardiac or respiratory dysfunction).
• 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:
  • Elevated liver function tests, including total bilirubin (TBILI) > 1.5× the upper limit of normal (ULN; unless subject has documented Gilbert's disease), aspartate aminotransferase (AST) or alanine aminotransferase (ALT) > 3.0×ULN;
  • Subjects with both a creatinine > 1.5×ULN and an estimated creatinine clearance of < 60 mL/min (using the Cockcroft-Gault equation);
  • Hemoglobin < 10 g/dL; platelet < 100×109/L; absolute neutrophil count < 1.5×109/L.
• 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).
• Prior cancers, except 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.
• Immunomodulatory therapy, (in order of increasing washout period) as follows:
  • Treatment with corticosteroids within 2 weeks of providing informed consent;
  • Treatment with glatiramer acetate or IFNβ within 4 weeks of providing informed consent;
  • Treatment with dimethyl fumarate within 4 weeks of providing informed consent;
  • Treatment with a B-cell depleting agent within 6 months of providing informed consent;
  • Treatment with methotrexate, azathioprine, or cyclosporine within 6 months of providing informed consent;
  • Treatment with fingolimod within 9 months of providing informed consent;
  • Treatment with natalizumab within 12 months of providing informed consent;
  • Treatment with teriflunomide within 12 months of providing informed consent unless patient has completed an accelerated clearance with cholestyramine;
  • Treatment with mitoxantrone, cyclophosphamide, cladribine, or any other immunosuppressant or cytotoxic therapy within 12 months of providing informed consent, or determined by the investigator to have residual immune suppression from these treatments;
  • Any previous treatment with alemtuzumab.
• Antithymocyte globulin or similar anti-T cell antibody therapy ≤ 4 weeks of providing informed consent.
• Female of childbearing potential unwilling to use a highly effective method of contraception (ie, one that results in pregnancy less than 1% per year when used consistently and correctly), eg, implants, injectables, combined oral contraceptives, some intrauterine contraceptive devices, sexual abstinence, or a vasectomized partner, and/or unwilling to refrain from donating eggs while undergoing treatment with ATA188 and for 3 months after the last dose OR Men with a female partner of childbearing potential unwilling to use a highly effective contraceptive measure and/or unwilling to refrain from donating sperm while undergoing treatment with ATA188 and for 3 months after the last dose.
• Women who are breastfeeding.
• Pregnancy.
• Inability to comply with study procedures.
• Previous treatment with EBV T cell therapy.