a Clinical Research of Sequential CAR-T Bridging HSCT in the Treatment of Relapse/Refractory B-cell Malignancies

Inclusion Criteria: 1. CD19-expressing or CD20-expressing relapsed or refractory B cell malignancies after at least one standard chemotherapy and one salvage regimen.According to current traditional therapies, there must be no available alternative curative therapies. 2. Patients enrolled must have an evaluated score above 60 with KPS. 3. Expected survival time of patients enrolled is over 3 months. 4. Gender is not limited, age from 14 years to 75 years. 5. Patients must have measurable or evaluable disease at the time of enrollment, which may include any evidence of disease including minimal residual disease detected by flow cytometry, cytogenetics, or polymerase chain reaction (PCR) analysis. 6. Adequate absolute CD3 count estimated need to be assured for obtaining target cell dose based on dosage cohorts. 7. Subjects with the following CNS status are eligible only in the absence of neurologic symptoms suggestive of CNS leukemia, such as cranial nerve palsy: CNS 1, defined as absence of blasts in cerebral spinal fluid (CSF) on cytospin preparation, regardless of the number of WBCs; CNS 2, defined as presence of \< 5/uL WBCs in CSF and cytospin positive for blasts, or \> 5/uL WBCs but negative by Steinherz/Bleyer algorithm CNS3 with marrow disease who has failed salvage systemic and intensive IT chemotherapy (and therefore not eligible for radiation) 8. Patients with isolated CNS relapse will be eligible if they have previously been treated with cranial radiation (at least 1800 cGy). 9. Ability to give informed consent. 10. Females of child-bearing potential must have a negative pregnancy test because of the potentially dangerous effects on the fetus. 11. Cardiac function: Left ventricular ejection fraction greater than or equal to 40% by MUGA or cardiac MRI, or fractional shortening greater than or equal to 28% by ECHO or left ventricular ejection fraction greater than or equal to 50% by ECHO. 12. Renal function: Creatinine level of peripheral blood is required no greater than 133umol/L. 13. Patients with history of allogeneic stem cell transplantation are eligible if there is no evidence of active GVHD and no longer taking immunosuppressive agents for at least 30 days prior to enrollment. 14. Patients volunteer to participate in the research. Exclusion Criteria: \- Subjects meeting any of the following criteria are not eligible for participation in the study: 1. Patients are evaluated below 50 scores with KPS. 2. Evident signs suggesting that patients are potentially allergic to cytokines. 3. Frequent infection history and recent infection is uncontrolled. 4. Patients with concomitant genetic syndrome: patients with Down syndrome, Fanconi anemia, Kostmann syndrome, Shwachman syndrome or any other known bone marrow failure syndrome 5. Active acute or chronic graft-versus-host disease (GVHD) or requirement of immunosuppressant medications for GVHD within 4 weeks of enrollment. 6. Concurrent use of systemic steroids or chronic use of immunosuppressant medications. Recent or current use of inhaled steroids is not exclusionary. For additional details regarding use of steroid and immunosuppressant medications. 7. Pregnancy and nursing females. HIV infection. 8. Active hepatitis B or active hepatitis C. 9. Participation in a prior investigational study within 4 weeks prior to enrollment or longer if required by local regulation. Participation in non-therapeutic research studies is allowed. 10. Class III/IV cardiovascular disability according to the New York Heart Association Classification. 11. Patients with a known history or prior diagnosis of other serious immunologic, malignant or inflammatory disease. 12. Other situations we think not eligible for participation in the research.