Recipient Inclusion Criteria:

          -  Histologically or cytologically confirmed relapsed acute myeloid leukemia (AML) or
             myelodysplastic syndrome (MDS), including any AML subtype, except acute promyelocytic
             leukemia (APL).

          -  Patients must have peripheral blast count ≤ 20,000/mm3. Use of hydroxyurea to control
             blast count is permitted.

          -  Patients must be status post-1st allo-HCT (including: matched related, matched
             unrelated, haploidentical, mismatched unrelated; and cord blood HCT).

          -  Eastern Cooperative Oncology Group (ECOG) performance status (PS) ≤ 2

          -  Adequate organ function, defined as:

               -  Hepatic transaminase (both alanine aminotransferase (ALT) and aspartate
                  aminotransferase (AST) levels ≤2.5 times the institutional upper limit of normal
                  (ULN),

               -  Total bilirubin level ≤1.5 times the ULN (unless the patient has a history of
                  Gilbert's Syndrome, in which case, total bilirubin must be ≤2.5 times the ULN),

               -  Creatinine clearance of ≥50 ml/min

               -  Adequate organ reserve including cardiovascular (ejection fraction within
                  institutional normal limits), pulmonary (baseline pulmonary function test [PFT]:
                  carbon monoxide diffusion capacity in the lung [DLCO] > 50%, forced expiratory
                  volume in 1 second [FEV1] > 70%), renal, and hepatic functioning sufficient, in
                  the judgment of the Investigator, to undergo therapy.

               -  Normal thyroid function or stable thyroid tests on supplementation, except
                  euthyroid sick syndrome.

          -  Recovery from toxicities of clinical consequence attributed to previous chemotherapy
             to CTCAE v4.0 Grade ≤ 1 (i.e., certain toxicities such as alopecia will not be
             considered in this category).

          -  Female patients of childbearing potential must test negative for pregnancy at
             enrollment and during the study. Sexually active women of child-bearing potential,
             unless surgically sterile, must be willing to use a highly effective method of birth
             control defined as those which result in a low failure rate (i.e., less than 1% per
             year) such as implants, injectables, combined oral contraceptives, intra-uterine
             devices (IUDs) or vasectomized partner. Male patients with partners of childbearing
             potential must be either vasectomized or agree to use a condom in addition to having
             their partners use another method of contraception resulting in a highly effective
             method of birth control defined as those which result in a low failure rate (i.e.,
             less than 1% per year) such as implants, injectables, combined oral contraceptives, or
             IUDs. Patients should not have sexual intercourse with females who are either pregnant
             or lactating without a condom. Contraception should be employed from the time of
             consent through 12 weeks after MGD006 administration. Patients should also abstain
             from sperm/egg donation during the course of the study.

          -  Able to have corticosteroids weaned to ≤0.5mg/kg prednisone/day (or equivalent)

          -  Able to have non-steroidal immunosuppression discontinued, including:

               -  mycophenolate (MMF)

               -  calcineurin inhibitors (tacrolimus, cyclosporine)

                  **calcineurin inhibitors must be able to be discontinued at least 14 days prior
                  to enrolling on study.

               -  JAK inhibitors (ruxolitinib)

               -  MTOR inhibitors (sirolimus)

          -  At least 18 years of age.

          -  Ability to understand and willingness to sign an IRB approved written informed consent
             document

        Recipient Exclusion Criteria:

          -  Active GVHD

          -  Currently receiving any other investigational agents.

          -  Any active untreated autoimmune disorders (with the exception of vitiligo, resolved
             childhood atopic dermatitis, prior Grave's disease now euthyroid clinically and with
             stable supplementation).

          -  Second primary malignancy that requires active therapy (adjuvant hormonal therapy is
             allowed).

          -  Antitumor therapy (chemotherapy, radiotherapy, antibody therapy, molecular- targeted
             therapy, retinoid therapy, or investigational agent) within 14 days or 5 half-lives of
             Cycle 1 Day 1, whichever is longer.

          -  At the time of study entry, steroids >0.5mg/kg of prednisone or equivalent (except
             steroid inhaler, nasal spray or ophthalmic solution which are allowed).

          -  Use of immunosuppressant medications (other than steroids as noted) in the 2 weeks
             prior to study drug administration (Cycle 1 Day 1).

          -  Isolated extramedullary relapse (i.e., no evidence of bone marrow involvement).

          -  Known central nervous system (CNS) leukemia. Patients with suspected CNS leukemia must
             be evaluated by lumbar puncture and be free of CNS disease prior to study entry.
             Previously treated CNS leukemia is allowed provided adequate treatment has been
             provided and the patient is free of CNS disease.

          -  Any medical or psychiatric condition limiting full compliance or increasing the safety
             risk, at the discretion of the PI, such as:

               -  active uncontrolled infection (including, but not limited to viral, bacterial,
                  fungal, or mycobacterial infection),

               -  known human immunodeficiency virus infection,

               -  known, active, or chronic hepatitis B or C infection (appropriately treated
                  HBV/HCV infections with documented clearance of viral titer are allowed),

               -  Grade 3 or 4 bleeding,

               -  significant pulmonary compromise including the requirement for supplemental
                  oxygen, history of non-infectious pneumonitis (including radiation pneumonitis),
                  pulmonary fibrosis, or severe chronic obstructive pulmonary disease (COPD),

               -  uncontrolled (persistent) hypertension (systolic pressure > 180 mm Hg or
                  diastolic pressure > 100 mm Hg

               -  clinically significant arrhythmia, clinically significant baseline QTcF >480
                  msec,

               -  unstable angina,

               -  recent myocardial infarction within 6 months prior to study drug administration
                  (Cycle 1 Day 1),

               -  clinically significant heart disease, such as, congestive heart failure, history
                  of pericarditis, myocarditis,

               -  history of stroke or transient ischemic event within 3 months prior to study drug
                  administration (Cycle 1 Day 1),

               -  untreated pulmonary embolism, or non-catheter-related deep-vein thrombosis in the
                  3 months prior to study drug administration (Cycle 1 Day 1),

               -  pregnancy, or breast feeding,

               -  major surgery or trauma within 4 weeks before enrollment.

          -  Known hypersensitivity to murine, yeast, or recombinant proteins; polysorbate 80;
             recombinant human serum albumin; benzyl alcohol; or any excipient contained in the
             MGD006 drug formulation.

          -  Dementia or altered mental status that would preclude sufficient understanding to
             provide informed consent.