 After signing informed consent, patients will undergo screening tests and procedures to determine eligibility. Once patient eligibility is confirmed, patients will have cells collected by leukapheresis to obtain peripheral blood mononuclear cells PBMC for CART22 manufacturing, unless adequate numbers of cells are available from a prior apheresis. Cells will be transduced with the anti-CD22 TCRζ4-1BB lentiviral vector, expanded in vitro and then frozen for future administration. Cryopreserved historical apheresis products collected from the patient prior to study entry are usable for CART22 manufacturing if collected at an appropriately certified apheresis center and the product meets adequate mononuclear cell yields. If a historical apheresis product is not available, an apheresis procedure will be scheduled for cell procurement after study entry. 