This study aims to explore the safety, tolerability, cellular kinetics, and pharmacodynamics of P-CD19CD20-ALLO1 in participants with progressive multiple sclerosis (PMS) and relapsing multiple sclerosis (RMS).

Inclusion Criteria:

• Age 18-60 years (inclusive) at the time of signing Informed Consent Form
• Diagnosis of progressive MS according to the revised McDonald 2017 criteria, and:

Expanded disability status scale (EDSS) score at screening, from 3 to 6 inclusive Evidence of disability progression and no relapses in the 2 years prior to screening

- Diagnosis of relapsing MS according to the revised McDonald 2017 criteria, and: Evidence of clinical relapses and MRI activity within two years prior to screening while on a disease modifying therapy

• EDSS score at screening, from 0 to 6 inclusive
• No relapses within 45 days of screening

Exclusion Criteria:

• Pregnant or breastfeeding, or intention of becoming pregnant within the timeframe in which contraception is required
• Participants who have confirmed or suspected Progressive Multifocal Leukoencephalopathy (PML)
• Known or suspected history of Hemophagocytic Lymphohistiocytosis/ Macrophage Activation Syndrome (HLH/MAS) or neurotoxicity with prior therapies
• Known presence of other neurologic disorders that may mimic MS
• History of currently active primary or secondary (non-drug-related) immunodeficiency
• Significant or uncontrolled medical disease which would preclude patient participation
• High risk for clinically significant bleeding or any condition requiring plasmapheresis, IV Ig, or acute blood product transfusions
• History of recurrent serious infections or chronic infection
• Prior treatment with CAR T-cell therapy, gene-therapy product, total body irradiation, bone marrow transplantation, allograft organ transplant, or hematopoietic stem cell transplant at any point
• Any previous treatment with immunomodulatory or immunosuppressive medication without an appropriate washout period.
• Inability to complete an MRI scan