A Study of KYV-101, a CD19 CAR T Cell Therapy, in Participants With Treatment Refractory Progressive Multiple Sclerosis

Inclusion Criteria: 1. Participant must sign a written informed consent form (ICF) prior to any screening procedures. 2. Participant must be 25-70 years of age (inclusive). 3. Clinical diagnosis of MS with evidence of primary or secondary progressive MS based on 2017 International Panel Criteria (Thompson 2018). 4. Historical documented presence of CSF restricted OCBs or elevated IgG Index (reconfirmed on screening). 5. Expanded disability status score (EDSS) score 3.0-7.0 6. Documented evidence of clinical disability progression within the 2 years prior to inclusion, i.e. a) progression of EDSS during the past two years of at least 1 point sustained for at least 6 months if inclusion EDSS is from 3.5 to 5.5 or at least 0.5 point increase sustained for at least 6 months if inclusion EDSS is from 6 to 6.5 or b) increase of Timed Walk 25 (TW25) by at least 20% in the last two years sustained for at least 6 months or c) other well-documented objective worsening despite at least 1 year of prior treatment for progressive forms of MS (including siponimod, and/or anti- B-lymphocyte antigen (CD20) MAb). 7. Adequate organ function as per below: Hematology- Hemoglobin \> 8 g/dl (without prior red blood cell transfusion within 7 days before the laboratory test) Platelets \> 50,000/µL (without transfusion support within 7 days before the laboratory test) Absolute Neutrophil Count (ANC) \>1,000/µL (prior growth factor support is permitted but must be without support in the 7 days prior to the laboratory test) Absolute Lymphocyte Count (ALC) \> 500/µL IgG \> 600 mg/dL Hepatic- Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 1.5 ×upper limit of normal (ULN) Total bilirubin ≤ 1.5 mg/dl, except with Gilbert's syndrome Renal- estimated Glomerular Filtration Rate (eGFR) \> 45 mL/min/1.73 m2 (measured by Chronic Kidney Disease (CKD) - Epidemiology Collaboration (EPI) 2021 equation) 8. Positive varicella zoster virus titer. Participants who test seronegative for varicella zoster virus IgG antibodies will be recommended to obtain vaccination prior to Investigational Product (IP) infusion. 9. Participants are recommended to be up to date on other recommended vaccinations, including against Coronavirus Disease (COVID-19)/ Severe Acute Respiratory Syndrome (SARS) Coronavirus 2 (CoV-2), per Centers for Disease Control and Prevention or institutional guidelines for immune-compromised individuals. 10. Women of childbearing potential must have a negative pregnancy test at screening, prior to apheresis, and prior to lymphodepletion chemotherapy using a highly sensitive serum pregnancy test (β- human Chorionic Gonadotropin (hCG)). A woman of childbearing potential is defined as a sexually mature woman who has not undergone a hysterectomy or tubal ligation or who has not been naturally postmenopausal for at least 24 consecutive months. 11. Female participants of childbearing potential who have a fertile male sexual partner must agree to use a highly effective method of contraception (failure rate of \< 1% per year when used consistently and correctly) from the time of signing the ICF until 24 months after the KYV-101 infusion. Examples of highly effective method of contraception include: * Established use of hormonal methods of contraception associated with inhibition of ovulation (e.g. oral, inserted, injected, implanted, transdermal), provided the participant or male participant's female partner plans to remain on the same treatment throughout the entire study and has been using that hormonal contraceptive for adequate time to ensure effectiveness. * Correctly placed copper containing- intrauterine device or intrauterine hormone-replacing system. * Female sterilization (bilateral tubal ligation/bilateral salpingectomy or bilateral tubal occlusive procedure (with confirmed occlusion). * Sexual abstinence, defined as completely and persistently refraining from all heterosexual intercourse (including during the entire period of risk associated with the study treatments) may obviate the need for contraception only if this is the preferred and usual lifestyle of the participant. 12. Male participants, if not surgically sterilized, must agree to use a highly effective method of contraception until 12 months post IP infusion. 13. Women and men must agree not to donate eggs (ova, oocytes) or sperm, respectively, until at least 12 months after receiving a KYV-101 infusion. 14. Ability to obtain adequate vascular access for leukapheresis procedure (either peripheral line or surgically placed line). Exclusion Criteria: 1. MS clinical stability on Disease Modifying Therapy (DMT) therapy. 2. Clinical relapse in the two years prior to study entry. 3. Disease other than MS to explain the first demyelinating event; including Aquaporin-4 (AQP4) IgG or Myelin oligodendrocyte glycoprotein (MOG)-IgG seropositivity. 4. Unwilling or unsafe to proceed with cerebral spinal fluid (CSF) exams based on coagulopathy or anatomy or other considerations in the judgment of the study investigator. 5. Unwilling or unsafe to proceed with MRI. 6. History of allogeneic or autologous stem cell transplant or solid organ transplant. 7. Prior treatment CAR-T or gene therapy product directed at any target. 8. Prior treatment with mitoxantrone, cladribine or alemtuzumab. 9. Need for ongoing anticoagulation. 10. Presence of hypogammaglobulinemia defined as IgG \< 600 mg/dL. 11. Plan to receive live, attenuated vaccine after signing ICF (inactive vaccines, like the influenza vaccine, are allowed). 12. Unable to interrupt autoimmune disease therapy prior to apheresis 13. Serologic status reflecting active hepatitis B or C infection. Patients who are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment. (PCR positive patients will be excluded.) Patients who are positive for hepatitis B core antibody will be required to remain on appropriate prophylactic antiviral therapy (e.g. with entecavir) for the duration of the study. 14. Positive serology for human immunodeficiency virus (HIV). 15. History of progressive multifocal leukoencephalopathy. 16. Untreated active or untreated latent tuberculosis or documented completed treatment without a negative chest X-ray (CXR) that shows no evidence of active Tuberculosis (TB). 17. Primary immunodeficiency as defined by a known genetic disorder. 18. History of splenectomy. 19. Impaired cardiac function or clinically significant cardiac disease including: 1. Unstable angina or myocardial infarction or coronary artery bypass graft (CABG) within 6 months prior to apheresis. 2. New York Heart Association (NYHA) stage III or IV congestive heart failure. 3. History of clinically significant cardiac arrhythmia (eg, ventricular tachycardia), complete left bundle branch block, high-grade atrioventricular (AV) block, or QT prolongation. 4. Inadequate cardiac function defined as left ventricular ejection fraction (LVEF) \< 40% as assessed by echocardiogram within 3 months of screening. Repeat testing may occur at Investigator's discretion. 20. Previous or concurrent malignancy with the following exceptions: 1. Adequately treated basal cell or squamous cell carcinoma (adequate wound healing is required prior to screening). 2. In situ carcinoma of the cervix or breast, treated curatively and without evidence of recurrence for at least 3 years prior to screening. 3. A primary malignancy which has been completely resected, or treated, and is in complete remission for at least 5 years prior to screening. 21. Serious and/or uncontrolled medical condition that, in the investigator's judgment, would cause unacceptable safety risk, interfere with study procedures or results, or compromise compliance with the protocol, such as: 1. Active, uncontrolled, viral, bacterial, or systemic fungal infection. 2. Chronic viral, bacterial, or systemic fungal infection that may be reactivated during treatment. 3. Requirement of supplemental oxygen to maintain oxygen saturation. 4. Clinical evidence of dementia. 5. A thromboembolic event within 6 months prior to apheresis. 6. On anti-coagulation agents that would be unsafe to transiently hold for medical procedures. 7. Uncontrolled Diabetes Mellitus (DM) or Hypertension (HTN). 22. Major surgery within 4 weeks prior to apheresis or planned within 4 weeks after KYV-101 administration. For surgery planned after 4 weeks post KYV-101 administration, discuss with the investigator. 23. History of any other neurologic disorder or medical condition the investigator considers would increase the risk for the participant, including seizure disorders. 24. Contraindications or life-threatening allergies, hypersensitivity, or intolerance to KYV-101 or its excipients, including dimethyl sulfoxide; cyclophosphamide (CYC) or fludarabine (FLU); or tocilizumab. 25. Pregnant or breastfeeding; or plans to become pregnant or breastfeed within 24 months after receiving the KYV-101 infusion. 26. Unwilling to participate in long-term follow up for safety monitoring after CAR-T therapy.