IL-15 Super Agonist ALT-803 to Treat Relapse Of Hematologic Malignancy After Allogeneic SCT

Inclusion Criteria: * Relapse after previous allogeneic stem cell transplant for one of the following hematologic malignancies (acute myelogenous leukemia, acute lymphoblastic leukemia,myelodysplastic syndromes, lymphoma, myeloma, Chronic lymphocytic Leukemia, chronic myelogenous leukemia): * For non-CML, relapse will be defined based on disease specific morphologic criteria from a bone marrow biopsy and aspirate or recurrence of disease specific cytogenetics. For disease specific definition of relapse, see appendix III. Relapse can be determined morphologically. Equivocal results for relapse should result in a repeated test after an appropriate time interval (suggested 1 month) to determine eligibility. * For CML, relapse will be defined as any cytogenetic evidence of a Philadelphia chromosome or persistence of BCR/ABL rearrangements by molecular testing on at least two measurements over a 6 month interval. If cytogenetics are normal and there is PCR evidence of a BCR/ABL fusion, patients will be eligible if they have evidence of a quantitative increase in CML measured either by quantitative PCR or by fluorescent in situ hybridization (FISH). For Chronic Phase CML patients only: * must have failed (no response in 3 months or incomplete response at 6 months) or refused treatment with a tyrosine-kinase inhibitor (TKI) * must have failed (defined as incomplete response or relapse) or refused DLI * Relapse must have occurred ≥ 60 days after transplant * Prior DLI is allowed, however not within the 30 days before the 1st dose of ALT-803 * Minimum donor chimerism of 10% * ≥ 18 years of age * Karnofsky performance status ≥ 70% (appendix II) * Adequate organ function within 14 days (30 days for cardiac and pulmonary) of enrollment defined as: * Creatinine: ≤ 2.0 mg/dL * Hepatic: SGOT/SGPT \< 5 x upper limit of institutional normal (ULN) * Thyroid Function: Thyroid Stimulating Hormone (TSH) within institutional normal range - patients with thyroid disease are eligible if euthyroid on suppressive or replacement therapy * Pulmonary: PFTs \> 50% of predicted * Cardiac: LVEF by ECHO or MUGA \> 40% * Ability to be off prednisone and other immunosuppressive drugs for at least 30 day before first dose of study drug * Patient agrees to stay within a reasonable distance (i.e. 30 miles) of the study site for the duration of the study treatment and for a minimum of 48 hours after the last dose and has a dedicated care giver as is standard practice for BMT outpatient care * Women of child bearing potential and men with partners of child bearing potential must agree to use effective contraception during therapy and for 4 months after completion of therapy * Voluntary written consent Exclusion Criteria: * Post-transplant lymphoproliferative diseases (often referred to as EBV-associated lymphomas) * Known active CNS leukemia or lymphoma - patients with previously treated CNS disease is permitted if neurologically stable with no ongoing or anticipated need for steroid therapy are eligible * Ongoing active acute or chronic GVHD requiring immunosuppressive therapy or signs of aGVHD or cGVHD requiring treatment * Pregnant or lactating - Women of child bearing potential must have a negative pregnancy test within 14 days of study treatment start * Class II or greater New York Heart Association Functional Classification criteria (appendix II) or serious cardiac arrhythmias likely to increase the risk of cardiac complications of cytokine therapy (e.g. ventricular tachycardia, frequent ventricular ectopy, or supraventricular tachyarrhythmia requiring chronic therapy * Marked baseline prolongation of QT/QTc interval (e.g. demonstration of a QTc interval greater than 500 milliseconds) * New progressive pulmonary infiltrates on screening chest x-ray or chest CT scan for which evaluation with bronchoscopy is not feasible. Infiltrates attributed to infection must be stable/improving (with associated clinical improvement) after 1 week of appropriate therapy (4 weeks for presumed or documented fungal infections). * Active bacterial, fungal, or viral infections - all prior infections must have resolved following optimal therapy * Positive hepatitis C serology or active hepatitis B infection because of the risk of hepatic inflammation and the possible confounding of drug toxicity assessment - chronic asymptomatic viral hepatitis is allowed * HIV positive because the effect of IL-15 viral loads, HIV immunity, and infectivity of proliferating T cells is unknown * History of severe asthma, presently on chronic medications (a history of mild asthma not requiring therapy is eligible)