Pracinostat and Gemtuzumab Ozogamicin (PraGO) in Patients With Relapsed/Refractory Acute Myeloid Leukemia

Inclusion Criteria: 1. Morphologically documented AML or secondary AML \[from prior conditions such as myelodysplastic syndrome (MDS), myeloproliferative neoplasm (MPN)\] or therapy related AML (t-AML), as defined by World Health Organization (WHO) criteria. 2. Age ≥60 years, with relapsed/refractory AML to at least one line of therapy. Patients with antecedent MDS who progressed to AML while on hypomethylating agent therapy will also be eligible. 3. Age 18-59 years with relapsed/refractory AML to at least two lines of intensive induction chemotherapy, or one line of therapy if deemed unsuitable for further intensive chemotherapy. 4. Patients aged 18 years or older with relapsed AML after allogeneic hematopoietic cell transplantation, if deemed unsuitable for further intensive chemotherapy. 5. Detectable CD33 expression on AML blasts confirmed by flow cytometry. 6. Karnofsky performance status ≥ 60 (or Eastern Cooperative Oncology Group (ECOG) Performance Score (PS) of 2 or less). 7. Adequate organ system function as outlined below: * Total bilirubin ≤ 2 x upper limit of normal (ULN), aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x ULN. * Serum creatinine ≤ 2 or a serum creatinine clearance ≤ 1.5 x ULN. * Baseline EKG with QT-interval corrected (QTcF) ≤ 450ms. 8. Females should be using adequate contraception, should not be breast feeding and must have a negative pregnancy test prior to start of dosing if of child-bearing potential. Male patient should avoid impregnating a female partner. It is not known what effects this treatment has on human pregnancy or development of the embryo or fetus. Therefore, female patients participating in this study should avoid becoming pregnant, and male patients should avoid impregnating a female partner. Non-sterilized female patients of reproductive age and male patients should use effective methods of contraception through defined periods during and after study treatment as specified below. Female patients must meet one of the following: * Postmenopausal for at least one year before the screening visit, or * Surgically sterile, or * If they are of childbearing potential, agree to practice two effective methods of contraception from the time of signing of the informed consent form through three months after the last dose of study drug, AND * Must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, or * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, post ovulation methods\] and withdrawal are not acceptable contraception methods.) Male patients, even if surgically sterilized (i.e., status post vasectomy), must agree to one of the following: * Practice effective barrier contraception during the entire study treatment period and through 90 days after the last study drug dose, OR * Must also adhere to the guidelines of any treatment-specific pregnancy prevention program, if applicable, OR * Agree to practice true abstinence when this is in line with the preferred and usual lifestyle of the subject. (Periodic abstinence (e.g., calendar, ovulation, symptothermal, postovulation methods\] and withdrawal are not acceptable methods of contraception.) 9. Ability to understand a written informed consent document, and the willingness to sign it. Exclusion Criteria: 1. Acute promyelocytic leukemia (APL). 2. Prior chemotherapy, radiotherapy, or investigative agent within 14 days, or within five half-lives of study entry. * Subjects must have recovered from side effects of prior treatment. * The use of hydroxyurea for leukoreduction prior to start of dosing is permitted. 3. Hematopoietic Stem Cell Transplantation (HCT) within 60 days of enrollment, or evidence of veno-occlusive disease (VOD) at any time post-transplant, or active graft-versus-host disease requiring systemic immunosuppressive therapy. 4. Life-threatening illness unrelated to AML, or any serious medical or psychiatric illness that could potentially interfere with participation in this study. 5. Active and uncontrolled human immunodeficiency virus (HIV), or chronic Hepatitis B, or Hepatitis C.