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

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

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

4. 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

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

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

7. ECOG scores 0 - 1;

8. Good cardiac and pulmonary organ function;

9. Expected survival time > 12 weeks;.

10. 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. Laboratory testing occurs when: including but not limited to, serum total bilirubin ≥1.5mg / dl; serum ALT or AST is 2.5 times higher than the upper limit of normal value; serum creatinine ≥2.0mg / dl; hemoglobin <80g / L; absolute neutrophil count <1000 / mm3 or dependent on GCSF or Other growth factors can maintain the centriole count ≥1000 / mm²; platelet count <50000 / mm³ or the above level can be maintained due to platelet transfusion;
3. Presence of clinically significant cardiovascular disease, such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or any heart function Grade 3 (moderate) or Grade 4 (severe) heart disease (according to the New York Heart Association Function Classification method: NYHA); patients with a history of myocardial infarction, cardiac angioplasty or stent implantation, unstable angina pectoris or other clinically significant heart disease within 12 months before enrollment;
4. A history of craniocerebral trauma, consciousness disorder, epilepsy, severe cerebral ischemia or hemorrhagic disease;
5. Need to 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. After allogeneic hematopoietic stem cell transplantation;
9. Plasma cell leukemia;
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.