This is an Open-label, Single Arm Study to Evaluate the Safety and Tolerability of Treatment With CT0591CP in Patients With Relapsed and/or Refractory Multiple Myeloma.

Inclusion Criteria: 1. Patients and legally acceptable representative must have voluntarily signed ICF and willing to complete the study procedure, after fully understanding of the study. 2. Age ≥ 18 years and ≤ 75 years, male or female. 3. The patients have received at least 3 prior regimens for MM. 4. Subjects should have received treatment with at least one proteasome inhibitor and one immunomodulatory drug (IMiD; and have been stable disease, relapsed or progressed after treatment with at least one regimen consisting of above-mentioned medications. 5. Subjects should have relapsed within 12 months after the last line of therapy, or not achieved at least minimal response (MR) or disease has progressed within 60 days after last line of therapy, with documented evidence. 6. Subjects should have measurable disease per IMWG 2016 criteria serum M-protein or urine M-protein are not measurable. 1） Serum M protein ≥ 5 g / L; 2） 24-hour urinary M-protein ≥ 200 mg; 3） The serum free light chain (sFLC) ratio was abnormal and the involved FLC ≥ 100mg/L in patients with light chain multiple myeloma whose serum or urinary M protein levels did not meet the assessable criteria. 7\. Expected survival \> 12 weeks. 8. Eastern Cooperative Oncology Group (ECOG) scores 0 - 1. 9. Subjects should have adequate function in hemostatic and liver and kidney. 10. Women of childbearing age must undergo a serum pregnancy test with negative results at screening and before lymphodepletion and be willing to use an effective and reliable method of contraception for at least 1 year after T cell infusion. All female subjects are prohibited from egg donation within 1 year after T cell infusion. 11\. Men must be willing to use an effective and reliable method of contraception for at least 1 year after T cell infusion if they have sexual activity with women of childbearing potential. All male subjects are prohibited from sperm donation within 1 year after T cell infusion. Exclusion Criteria: 1. Pregnant or lactating women. 2. Subjects positive for any following tests: human immunodeficiency virus (HIV) antibody, Treponema pallidum (syphilis) antibody, hepatitis C virus (HCV) antibody, 3. Active hepatitis B; HBV-DNA test must be below the lower limit of measurement. 4. Subjects with any uncontrolled active infection (Except for prophylactic treatment). 5. Subjects with AEs from previous treatment that have not recovered to Common Terminology Criteria for Adverse Events (CTCAE) v5.0 ≤ 1, excluding hair loss and other events that the treating physician considers as tolerable. 6. Subjects who have received autologous BCMA CAR-T therapy 7. Subjects who have had anti-BCMA therapy. 8. Subjects who have received allogeneic stem cell transplantation for MM. 9. Subjects who have received autologous stem cell transplantation less than 12 weeks before ICF. 10. Positive anti-HLA-II antibody specificity test 11. Subjects who have received any anti-MM treatment 14 days before ICF; the subjects are eligible to participate in the study regardless of the radiotherapy end date if the radiation area less than 5% of whole body. 12. Subjects who have received systemic glucocorticoids within 7 days before infusion, except inhaled steroids. 13. Subjects who have Waldenström macroglobulinemia, POEMS (polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin changes) syndrome or primary light chain amyloidosis. 14. Subjects who have been received live attenuated vaccine within 8 weeks or inactivated vaccine within 4 weeks before lymphodepletion. 15. Subjects allergic to or intolerant of fludarabine, cyclophosphamide, tocilizumab, or allergic to the ingredients (DMSO) of CT0591CP cell preparations; subject with confirmed another serious allergy history. 16. Subjects who have any uncontrolled disease conditions within 6 months prior to the signing of inform consent. 17. LVEF \< 50% 18. Blood oxygen saturation that can only be maintained at \> 95% by oxygen inhalation. 19. Subjects known to have active autoimmune diseases including but not limited to psoriasis, rheumatoid arthritis and other conditions that require long-term immunosuppressive therapy. 20. Subjects with second malignancies in addition to MM are not eligible if the second malignancy has required treatment within the past 5 years 21. Subjects who have central nervous system (CNS) metastases or symptomatic CNS involvement. 22. Subjects who are unable or unwilling to comply with the requirements of clinical trial or other reasons that are not suitable for participating in the clinical trial. 23. Subjects who have received major surgery 2 weeks prior to ICF or plan to receive major surgery within 4 weeks after cell infusion (excluding cataract and other local anesthesia). 24. Subjects who are related to investigator or study personnel, or with possible conflict of interest with the investigator or study personnel.