Inclusion Criteria:

          -  Written informed consent and HIPAA authorization for release of personal health
             information. NOTE: HIPAA authorization may be included in the informed consent or
             obtained separately. Patients must be capable of understanding the investigational
             nature, potential risks and benefits of the study and provide valid informed consent.

          -  Age ≥ 60 years at the time of consent who are deemed candidates (by their transplant
             physician) for reduced-intensity allogeneic PBSC transplantation. A recent randomized
             trial in patients aged 18-65 years demonstrated that myeloablative conditioning
             regimens are associated with improved overall survival in AML (largely due to a
             reduction in the risk of relapse), but resulted in equivalent survival in patients
             with MDS.4 However, it is acknowledged that some AML patients between 55-65 years may
             not tolerate myeloablative regimens due to associated comorbidities. Physicians should
             take the risks of the disease versus the patient's comorbidities in deciding on the
             appropriate preparative regimen in a given patient.

          -  Patients aged 18-59 years at the time of consent who are judged not to be candidates
             for myeloablative allogeneic PBSC transplantation by the transplant physician.

          -  Karnofsky performance status (KPS) ≥ 70%

          -  Patients must have any of the following hematological malignancies at the time of
             transplantation:

               -  Acute myeloid leukemia (AML) in first (CR1) or subsequent complete remission
                  (CR2, CR3 or beyond), as defined by less than 5% blasts in the bone marrow and
                  peripheral blood.

               -  Myelodysplastic disorder (MDS) of high or very high-risk according to the revised
                  International Prognostic Scoring System (IPSS-R).1

                    -  Patients with MDS should have the bone marrow and the peripheral blood blast
                       percentage reduced to <10% within at least 45 days of transplantation.

                    -  The type of cytoreduction therapy used is at the discretion of the treating
                       physician and may include use of hypomethylating drugs but not immune
                       checkpoint inhibitors.

                    -  Therapy-related MDS (regardless of IPSS score)

          -  Patients must receive a reduced-intensity conditioning (RIC) regimen as defined
             operationally by the National Marrow Donor Program and CIBMTR. RIC regimens are
             defined as those containing:

               -  ≤ 500 cGy total-body irradiation (TBI)

               -  ≤9 mg/kg total busulfan dose (PO or IV)

               -  ≤140 mg/m2 total melphalan dose

               -  ≤10 mg/kg total thiotepa dose

               -  Usually includes a purine analogue (fludarabine, cladribine, or pentostatin).

               -  Use of fludarabine and cyclophosphamide (up to 200 mg/kg total dose) is also
                  considered RIC.99

          -  Patients must have received GVHD prophylaxis with any of the regimens below. Accepted
             regimens are:

               -  Calcineurin inhibitor (tacrolimus or cyclosporine A) plus methotrexate

               -  Calcineurin inhibitor plus mycophenolate mofetil

               -  Calcineurin inhibitor plus sirolimus

               -  Post-transplant cyclophosphamide (PtCy) (in combination with calcineurin
                  inhibitor or sirolimus, plus mycophenolate mofetil)

          -  Patients receiving the above regimens should be beginning to taper immunosuppression
             drugs between days +100 to +120 (in the absence of acute GVHD) with the goal of
             discontinuing immunosuppression by approximately day +180 as tolerated and according
             to institutional standards.

          -  Stem cell source must be mobilized peripheral blood (i.e., PBSC) and not bone marrow
             or cord blood.

          -  Allogeneic grafts from 6/6 HLA-matched siblings or from 10/10 HLA allele matched
             volunteer unrelated donors (matched for at least HLA-A, B, C and DRB1 and DQB1 by high
             resolution typing) are included.

          -  Are in complete remission defined as having <5% blasts in the bone marrow with normal
             karyotype and no extramedullary disease. This should be documented on a bone marrow
             biopsy performed within 14 days before study registration.

          -  Absolute neutrophil count (ANC) >1.5x109/l

          -  Platelet count >100x109/l (with no platelet transfusions in past 7 days)

          -  Serum creatinine <2.0 mg/dl

          -  Serum bilirubin < 2 x upper limit of normal

          -  AST and ALT <2.5 x upper limit of normal

          -  Non-pregnant and non-nursing.

          -  Women are considered of childbearing potential (WOCBP) unless they are surgically
             sterile (have undergone a hysterectomy, bilateral tubal ligation, or bilateral
             oophorectomy) or are post-menopausal. Menopause is defined clinically as 12 months of
             amenorrhea in a woman over 45 in the absence of other biological or physiological
             causes.

          -  Women of childbearing potential must be willing to abstain from heterosexual activity
             or use an effective method of contraception from the time of informed consent until 5
             months after the last dose of study drug.

          -  Men who are sexually active with WOCBP must use any contraceptive method with a
             failure rate of less than 1% per year. Men receiving study drug and who are sexually
             active with WOCBP will be instructed to adhere to contraception from the first dose of
             study drug until 7 months after the last dose of study drug.

        Exclusion Criteria:

          -  Use of a myeloablative preparative regimen

          -  Active central nervous system (CNS) leukemia. Patients with prior CNS leukemia that is
             now in remission are eligible.

          -  Prior allogeneic or autologous stem cell transplantation before current transplant

          -  Use of bone marrow or cord blood as stem cell source

          -  History of acute GvHD of any grade

          -  Use of systemic corticosteroids within 28 days prior to registration (except for use
             as replacement for adrenal insufficiency).

          -  Uncontrolled bacterial, viral or fungal infection at time of registration (defined as
             currently taking medication and progression or persistence of clinical symptoms).
             Patients with prior infection (e.g., fungal infection) that is resolved but need
             continuing prophylaxis can be included.

          -  HIV infection or disease at time of transplant. Patients with immune dysfunction are
             at a significantly higher risk of infection from intensive immunosuppressive
             therapies. Infectious disease testing will be performed according to local practice.

          -  Known additional malignancy that is active and/or progressive requiring treatment;
             exceptions include basal cell or squamous cell skin cancer, in situ cervical or
             bladder cancer, or other cancer for which the subject has been disease-free for at
             least three (3) years.

          -  Patients who have received a live/attenuated vaccine within 30 days of first expected
             treatment with nivolumab. However, it is recommended that patients who have received
             an allogeneic transplant should not receive live/attenuated vaccines within two years
             after allogeneic transplantation.