Inclusion Criteria:

1. Patients must be considered appropriate candidates for either the low- or high-intensity conditioning regimen for allogeneic hematopoietic stem cell transplantation based on the following age-related criteria:

1. Age 50-70 years old or
2. Age 18-49 and unfit for a conventional myeloablative conditioning regimen per the treating physician
2. Patients have one of the following diagnoses:

1. Acute lymphocytic leukemia (ALL) in first or subsequent morphological remission (\<5% marrow blasts by morphology).
2. Acute myeloid leukemia (AML) in first or subsequent morphological remission (\<5% marrow blasts by morphology) with or without hematologic recovery.
3. Other acute leukemia or related neoplasm (including but not limited to 'mixed phenotype' 'biphenotypic', 'acute undifferentiated' or 'ambiguous lineage' acute leukemia, blastic plasmacytoid dendritic cell neoplasm, lymphoblastic lymphoma, Burkitt leukemia/lymphoma, mast cell leukemia or chronic myeloid leukemia with blast crisis) in first or subsequent morphological remission (\<5% marrow blasts by morphology) with or without hematologic recovery.
4. Myelodysplastic syndrome (MDS) with a history of excess blasts, with \>5% marrow blasts by morphology after receiving at least one cycle of treatment, including but not limited to hypomethylating agent, BCL-2 inhibitor, cytoreductive chemotherapy.
5. High-risk myeloproliferative neoplasm (MPN) with no evidence of high-grade bone marrow fibrosis or massive splenomegaly at the time of enrollment.
3. Patients with an 8/8 HLA-matched (HLA-A, B, C, DRB1) related or unrelated donor capable of donating peripheral blood stem cells (PBSC)
4. Provision of signed and dated informed consent form
5. Sexually active fertile subjects and their partners must agree to use highly effective methods of contraception prior to study entry, during the course of the study, and until tacrolimus or other immunosuppressive therapy for GVHD is discontinued (whichever is later). An additional contraceptive method, such as a barrier method (e.g., condom), is required. In addition, men must agree not to donate sperm and women must agree not to donate eggs (ova, oocyte) for the purpose of reproduction during these same periods.
6. Female subjects of childbearing potential must not be pregnant or breastfeeding at screening. Female subjects are considered to be of childbearing potential unless one of the following criteria is met:

1. Permanent sterilization (hysterectomy, bilateral salpingectomy, or bilateral oophorectomy) or documented postmenopausal status (defined as 12 months of amenorrhea in a woman \> 45 years-of-age in the absence of other biological or physiological causes). Note: Documentation may include review of medical records, medical examination, or medical history interview by study site staff.

Exclusion Criteria:

Subjects will be excluded from the study if they meet any of the following criteria.

For high-intensity regimen:

1. Poor performance status with Karnofsky Score \<70%
2. Center for International Blood and Marrow Transplant Research (CIBMTR) hematopoietic cell transplant co-morbidity index (HCT-CI) score \>5
3. Patients with active central nervous system (CNS) involvement refractory to intrathecal chemotherapy and/or standard craniospinal radiation.
4. Patients who are positive for HIV-1, HIV-2, HTLV1 or HTLV2.
5. Patients with uncontrolled infections for whom alloSCT is considered contraindicated by the consulting infectious disease physician.
6. Patients with organ dysfunction, including:

1. Renal insufficiency creatinine clearance \<45 ml/min/1.72m2 measured by 24-hr urine specimen
2. Left ventricular ejection fraction \<45%
3. Diffusing capacity of the lung for carbon monoxide (DLCO) corrected \<50% or FEV1 \<50%
4. Liver function abnormality: total bilirubin, aspartate aminotransferase (AST), and alanine aminotransferase (ALT) \>5 times the upper limit of normal should be evaluated by a gastroenterologist. If a gastroenterologist considers that alloSCT is contraindicated, the patient will be excluded from the protocol.
7. Patients who have received previous allogeneic transplantation.
8. Patients with a life expectancy \<12 months due to co-existing diseases other than hematologic malignancies.
9. Patients with any other significant medical conditions that would make them unsuitable for transplantation, as determined by the PI.
10. Patients with a known hypersensitivity to cyclophosphamide, thiotepa, fludarabine, busulfan, tacrolimus, or mycophenolate mofetil (MMF).
11. Patients who have received checkpoint inhibitors within three months of transplantation, unless an exception is made by the PI.

For low-intensity regimen

1. Poor performance status with Karnofsky Score \<60%
2. Patients with active CNS involvement refractory to intrathecal chemotherapy and/or standard craniospinal radiation.
3. Patients who are positive for HIV-1, HIV-2, HTLV1 or HTLV2.
4. Patients with uncontrolled infections for whom alloSCT is considered contraindicated by the consulting infectious disease physician.
5. Patients with organ dysfunction, including:

1. Renal insufficiency creatinine clearance \<40 ml/min/1.72m2 measured by 24-hr urine specimen
2. Left ventricular ejection fraction \<40%
3. DLCO corrected\< 50% or FEV1\<50%
4. Liver function abnormality: total bilirubin, AST, ALT\>5 times the upper limit of normal should be evaluated by a gastroenterologist. If a gastroenterologist considers that alloSCT is contraindicated, the patient will be excluded from the protocol.
6. Patients who have received previous allogeneic transplantation.
7. Patients with a life expectancy \<12 months from co-existing disease other than hematologic malignancies
8. Patients with any other significant medical conditions that would make them unsuitable for transplantation, as determined by the PI.
9. Patients with a known hypersensitivity to cyclophosphamide, thiotepa, fludarabine, busulfan, tacrolimus, or mycophenolate mofetil (MMF).
10. Patients who have received checkpoint inhibitors within three months of transplantation, unless an exception is made by the PI.