A Study of CD20/CD22 Targeted CAR T-cell Therapy for Relapsed or Refractory Lymphoid Malignancies

Criteria: Inclusion Criteria: Inclusion criteria applicable to ALL only: 1. Male or female aged ≥ 3 and \<70 years old; 2. Histologically confirmed diagnosis of CD19+ B-ALL per the US National Comprehensive Cancer Network (NCCN) Clinical Practice Guidelines for Acute Lymphoblastic Leukemia (2016.v1); 3. Relapsed or refractory CD19+ B-ALL (meeting one of the following conditions): 1. CR not achieved after standardized chemotherapy; 2. CR achieved following the first induction, but CR duration is ≤ 12 months; 3. Ineffective after first or multiple remedial treatments; 4. 2 or more recurrences; 4. The number of primordial cells (lymphoblast and prolymphocyte) in bone marrow is \>5% (morphology) and/or \>1% (Flow cytometry); 5. Philadelphia-chromosome-negative (Ph-) patients; or Philadelphia-chromosome- positive (Ph+) patients who cannot tolerate TKI treatments or do not respond to 2 TKI treatments; Inclusion criteria applicable to NHL only: 1. Male or female aged ≥ 18 and \<70 years old; 2. Histologically confirmed diagnosis per WHO Classification Criteria for Lymphocytic Tumors 2016, including DLBCL(NOS), follicular lymphoma, Chronic lymphoblastic leukemia/small lymphoblastic lymphoma transforms DLBCL, PMBCL and high grade B cell lymphoma; 3. Relapsed or refractory DLBCL (meeting one of the following conditions): 1. No remission or recurrence after receiving second-line or above second-line chemotherapy; 2. Primary drug resistance; 3. Recurrence after autologous hematopoietic stem cell transplantation; 4. According to Lugano 2014, there should be at least one evaluable tumor lesion. Applicable standards for ALL and NHL: 1. HLA antibody(-) or HLA antibody(+) and HLA donor specific antibody(DSA)(-); 2. total bilirubin ≤ 51umol/L, ALT and AST ≤ 3 times of upper limit of normal, creatinine ≤ 176.8umol/L; 3. Echocardiogram shows left ventricular ejection fraction (LVEF) ≥ 50%; 4. No active infection in the lungs, blood oxygen saturation by sucking air is ≥ 92%; 5. Estimated survival time ≥ 3 months; 6. ECOG performance status 0 to 2; 7. Patients or their legal guardians volunteer to participate in the study and sign the informed consent. Exclusion Criteria: 1. patients with extramedullary lesions, except those with CNSL (CNS-1) under effective control (for ALL patients only); 2. Confirmed diagnosis of lymphoblastic crisis of chronic myeloid leukemia, Burkitt's leukemia/lymphoma per WHO Classification Criteria (for ALL patients only); 3. Patients with hereditary syndrome such as Fanconi anemia, Kostmann syndrome, Shwachman syndrome or any other known bone marrow failure syndrome (for ALL patients only); 4. Patients with intracranial extralateral lesions (cerebrospinal fluid tumor cells and/or intracranial lymphoma invasion shown by MRI) (for NHL patients only) ; 5. Extensive involvement of gastrointestinal lymphoma (for NHL patients only); 6. Radiotherapy, chemotherapy and monoclonal antibody within 1 week before screening; 7. Have a history of allergy to any of the components in the cell products; 8. Prior treatment with any CAR T cell product or other genetically-modified T cell therapies; 9. According to the New York heart association (NYHA) cardiac function classification criteria, Subjects with grade III or IV cardiac insufficiency; 10. Myocardial infarction, cardioangioplasty or stenting, unstable angina pectoris, or other severe cardiac diseases within 12 months of enrollment; 11. Severe primary or secondary hypertension of grade 3 or above (WHO Hypertension Guidelines, 1999); 12. Electrocardiogram shows prolonged QT interval, severe heart diseases such as severe arrhythmia in the past; 13. History of craniocerebral trauma, conscious disturbance, epilepsy, cerebrovascular ischemia, and cerebrovascular hemorrhagic diseases; 14. Patients with severe active infections (excluding simple urinary tract infection and bacterial pharyngitis). 15. Indwelling catheters in vivo (e.g. percutaneous nephrostomy, Foley catheter, bile duct catheter, or pleural/peritoneal/pericardial catheter). Ommaya storage, dedicated central venous access catheters such as Port-a-Cath or Hickman catheters are allowed; 16. History of other primary cancer, except for the following conditions: 1. Cured non-melanoma after resection, such as basal cell carcinoma of the skin; 2. Cervical cancer in situ, localized prostate cancer, ductal cancer in situ with disease-free survival ≥ 2 years after adequate treatment; 17. Patients with autoimmune diseases requiring treatment, patients with immunodeficiency or requiring immunosuppressive therapy; 18. Patients with graft-versus-host disease (GVHD); 19. Prior immunizations with live vaccine 4 weeks prior to screening; 20. History of alcoholism, drug abuse or mental illness; 21. If HBsAg positive at screening, HBV DNA copy number detected by PCR in patients with active hepatitis B \> 1000 (if HBV DNA copy number≤1000, routine antiviral therapy is required after enrollment), as well as CMV, hepatitis C, syphilis infection; 22. Concurrent therapy with systemic steroids within 1 week prior to screening, except for the patients recently or currently receiving inhaled steroids; 23. Patients who have participated in any other clinical studies within 2 weeks prior to screening; 24. Pregnant and breast-feeding women and the subjects who are fertile and unable to take effective contraceptive measures (regardless of the gender); 25. Any situations that the investigator believes may increase the risk of patients or interfere with the results of study.