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), and including AML that has evolved from a previous MDS or MPN.
* Patients must have peripheral blast count ≤ 20,000/mm3. Use of hydroxyurea to control blast count is permitted.
* Patients must be status post 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 requiring systemic immunosuppresion with more than 0.5 mg/day prednisone
* 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.