A Study of Inotuzumab and Blinatumomab in People With B-cell Acute Lymphoblastic Leukemia

Inclusion Criteria: * Age ≥ 18 years of age. * Newly diagnosed CD19+ and CD22+ B-ALL with the following characteristics * Patients ≥55 years old, OR * Patients 18-54 years old who decline or are deemed unfit for conventional chemotherapy with at least one of the following criteria: * ECOG performance status of 2 or more * Severe cardiac comorbidity (including congestive heart failure requiring treatment) * Known pulmonary comorbidity (including DLCO ≤65% or FEV1 ≤65%) * Renal comorbidity (including creatinine clearance 30-45 mL/min) * Relapsed or refractory CD19+ and CD22+ B-ALL * Patients with extramedullary disease will be allowed as long as they have detectable disease by flow cytometry in the bone marrow * Peripheral absolute lymphoblast count of ≤ 10,000/ml after pre-phase (not required for enrollment but required to proceed with first dose of inotuzumab). * Philadelphia chromosome negative by FISH/karyotype for t(19;22) or RT PCR for bcr-abl transcript. * CD19 and CD22 expression will be confirmed by enrolling institutions prior to study registration by flow cytometry and/or IHC. * Creatinine clearance ≥30 mL/min * Total bilirubin ≤ 1.5 x upper limit of normal, AST and ALT ≤3.0x upper limit of normal (ULN) * QTcF ≤ 480 * Ejection fraction ≥ 50% Exclusion Criteria: * Patients with Burkitt's lymphoma, T-ALL, CML in lymphoid blast crisis and mixed phenotype acute leukemia (MPAL). * Patients with newly diagnosed B-ALL who received prior treatments, with the exceptio…