A Study to Evaluate the Safety, Tolerability, Cellular Kinetics, and Pharmacodynamics of P-CD19CD20-ALLO1 in Participants With Multiple Sclerosis

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