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)