Daratumumab for Chemotherapy-Refractory Minimal Residual Disease in T Cell ALL

Inclusion Criteria: * Patient must have documented T cell ALL and must be in first or later hematologic CR or CRi after a minimum of 2 blocks of intensive chemotherapy. * Patients in hematologic CR or CRi must have persistent or recurrent MRD ≥ 10-4. * Institution must have received central MRD status test results confirming persistent or recurrent MRD ≥ 10-4 by flow cytometry. * Patient may have undergone a prior allogeneic stem cell transplant, but patient may not have Grafts Versus Host Disease (GVHD) that requires ongoing immunosuppressive therapy. Patient may receive prednisone if the dose is ≤ 10 mg per day. * Patient must have an ECOG performance status 0-2. * All patients of childbearing potential must have a blood test or urine study within 14 days prior to Step 1 registration to rule out pregnancy. * Patients must not expect to conceive or father children by using an accepted and effective method(s) of contraception or by abstaining from sexual intercourse for the duration of their participation in the study and continue to 3 months after the last dose of protocol treatment. Patients must also agree to abstain from donating sperm, even if they have had a successful vasectomy, or donating eggs while on study treatment and for 3 months after the last dose of protocol treatment. * Patient must have the ability to understand and the willingness to sign a written informed consent document. Patients with impaired decision-making capacity (IDMC) who have a legally authorized representative (LAR) or caregiver and/or family member available will also be considered eligible. * Patient must have adequate organ and marrow function as defined below (these labs must be obtained ≤ 7 days prior to Step 1 registration). * Absolute neutrophil count (ANC) ≥ 750/μL * Platelets ≥ 75,000/μL * Total or Direct bilirubin ≤ 2 mg/dL * AST(SGOT)/ALT(SGPT) ≤ 3.0 × institutional ULN * Creatinine ≤ 1.5 x institutional ULN or Creatinine Clearance \> 30 ml/min * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of registration are eligible for this trial. * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Patients with prior CNS involvement are eligible as long as they do not have active CNS involvement at time of Step 1 registration. * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. * Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better. Exclusion Criteria: -Patient must not be pregnant or breast-feeding due to the potential harm to an unborn fetus and possible risk for adverse events in nursing infants with the treatment regimens being used