This is a single-center, non-randomized study to evaluate the safety and efficacy of C-CAR088 in relapsed or refractory multiple myeloma patient.

The study will include the following sequential phases: Screening, Pre-Treatment (Cell Product Preparation, Lymphodepleting Chemotherapy), C-CAR088 infusion and Follow-up.

Inclusion Criteria:

1. Volunteered to participate in this study and signed informed consent.

2. Age 18-70 years old, male or female.

3. Meet the internationally accepted Criteria for the diagnosis of multiple myeloma (IMWG diagnostic criteria 2014).

4. Patients with relapsed or refractory multiple myeloma who meet at least one of the following conditions:

   • Subjects must have received at least two therapy regimens (including proteasome inhibitor or immune-modulator therapy, disease progress or relapse after the last therapy).
   • Subjects have received only one therapy regimen, but the investigators judge that patients have unmet treatment needs or can't get benefit from current treatment options.

5. Subjects have one or more measurable multiple myeloma lesion, must include one of the following conditions:

   • Serum M protein≥1 g/dl(10g/L)
   • Urine M protein≥200 mg/24h
   • Serum free light chain(sFLC): κ/λ ratio abnormal and ≥10 mg/dl

6. Bone marrow sample is confirmed as BCMA-positive by flow cytometry or pathological examination.

7. At least 2 weeks from monoclonal antibody therapy prior to CAR T cell therapy.

8. ECOG scores 0 - 1.

9. Normal cardiac diastolic function, left ventricular ejection fraction (LVEF) ≥ 50% (detected by echocardiography), no serious arrhythmia.

10. No active pulmonary infections, normal pulmonary function and oxygen saturation ≥ 92% on room air.

11. No contraindications of leukapheresis.

12. Expected survival > 12 weeks.

13. Female subjects in childbearing age, their serum or urine pregnancy test must be negative,until 7 days before cell therapy and all subjects must agree to take effective contraceptive measures during the trial.

Exclusion Criteria:

1. Have a history of allergy to cellular products.
2. Any kind of these laboratory testing: including but not limited to,serum total bilirubin≧1.5mg/dl, serum ALT, AST≧2.5×ULN, serum creatinine≧2.0mg/dl, Hb (hemoglobin)<80g/L, neutrophils<1000/mm^3, platelets≦50000/mm^3 or platelet count maintained by transfusion.
3. Subjects with the following clinically significant cardiovascular diseases.
4. A history of craniocerebral trauma, consciousness disorder, epilepsy, severe cerebral ischemia or hemorrhagic disease.
5. Use any anticoagulant (except aspirin).
6. Patients requiring urgent treatment due to tumor progression or spinal cord compression.
7. Patients with CNS metastasis or symptoms of CNS involvement.
8. The investigators judge that any increase in the risk of the subject or interference with the results of the trial.
9. After allogeneic hematopoietic stem cell transplantation.
10. Plasma cell leukemia.
11. One week before leukapheresis and one week before CART cell infusion, treated with more than 5mg/d prednisone (or equal amount of other corticosteroids).
12. Subjects with any autoimmune disease or any immune deficiency disease or other disease in need of immunosuppressive therapy.
13. Uncontrolled active infection.
14. Prior treatment with CAR T therapy or any other genetically modified T cell therapy.
15. Live vaccine inoculation within four weeks before enrollment.
16. Hepatitis B or hepatitis C virus infection (including carriers), syphilis, as well as acquired, congenital immune deficiency diseases, including but not limited to HIV-infected persons.
17. Have a history of alcoholism, drug addiction and mental illness.
18. Participated in any other clinical trial within three months.
19. The investigators believe that there are other circumstances that are not suitable for the trial.