This is a single-center, non-randomized and dose-escalation 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. Age 18-75 years old, male or female;

2. The patient volunteered to participate in the study, and he or his legal guardian signed the Informed Consent;

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

4. Patients with a clear diagnosis of relapsed or refractory multiple myeloma；

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

   • Serum M protein≥1.0 g/dL(10g/L)
   • Urine M protein≥200 mg/24h
   • Serum free light chain(sFLC): κ/λ FLC ratio is abnormal and affected FLC ≥10mg / dL

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

7. ECOG scores 0 - 1;

8. Echocardiography showed normal diastolic function, left ventricular ejection fraction (LVEF) ≥50%, and no severe arrhythmia;

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

10. Absolute neutrophil count ≥1.0 × 109 / L, platelet count ≥50 × 109 / L; total serum bilirubin ≤1.5mg / dl; serum ALT or AST less than 2.5 times the upper limit of normal; serum creatinine ≤2.0mg / dl;

11. No contraindications of peripheral blood apheresis;

12. Expected survival time > 12 weeks;.

13. Female subjects of childbearing age must have a negative urine / blood pregnancy test within 7 days before cell therapy and not be in lactation; female or male subjects of childbearing age need to take effective contraception throughout the study.

Exclusion Criteria:

1. Have a history of allergy to cellular products;
2. Presence of clinically significant cardiovascular disease;
3. A history of craniocerebral trauma, consciousness disorder, epilepsy, severe cerebral ischemia or hemorrhagic disease;
4. Need to use any anticoagulant (except aspirin);
5. Patients requiring urgent treatment due to tumor progression or spinal cord compression;
6. Patients with CNS metastasis or symptoms of CNS involvement;
7. After allogeneic hematopoietic stem cell transplantation;
8. Plasma cell leukemia;
9. Received systemic anti-tumor treatment within 2 weeks before apheresis, and within 1 week before apheresis, prednisone (or equivalent amount of other corticosteroids) was applied in excess of 5 mg/d ;
10. Patients with autoimmune diseases, immunodeficiency, or other immunosuppressive agents;
11. Uncontrolled active infection;
12. Have used any CAR T cell products or other genetically modified T cell therapy before;
13. 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;
14. Have a history of alcoholism, drug addiction and mental illness;
15. Participated in any other clinical trial within 1 months;
16. The investigators believe that there are other circumstances that are not suitable for the trial.