Mismatched Transplantation Using High-dose Post-transplant Cyclophosphamide

Inclusion Criteria: 1. Patients \< 55 years (Myeloablative regimen #1) or \> 55 and \</= 75 years or significant comorbidities (Reduced intensity regimen #2) old lacking a matched related volunteer donor identified in time for transplant for which a related haploidentical donor (\</= 7/8 allele match at the A, B, C, DR loci), a 7/8 allele matched related or unrelated donor is identified, or a matched unrelated donor (MUD). The patients must be diagnosed with a high-risk disease defined as following: 2. Acute lymphocytic leukemia (ALL) in CR1 with high-risk features including adverse cytogenetics such as t(9;22), t(1;19), t(4;11), or MLL gene rearrangements; ALL in second or greater remission or ALL with relapsed disease, peripheral blood blasts \< 1000/microliter, ALL patients must show response to most recent received chemotherapy; 3. Acute myeloid leukemia (AML) in CR1 with intermediate-risk disease or high-risk features defined as: Greater than 1 cycle of induction therapy required to achieve remission; Preceding myelodysplastic syndrome (MDS) or myeloproliferative disease; Presence of FLT3 mutations or internal tandem duplications; FAB M6 or M7 classification; Adverse cytogenetics, -5, del 5q, -7, del7q, abnormalities involving 3q, 9q, 11q, 20q, 21q, 17, +8 \[\> 3 abnormalities\], peripheral blood blasts \<1000/microliter, AML patients must show response to most recent received chemotherapy; 4. AML in second or greater remission, primary induction failure and patients with relapsed disease, peripheral blood blasts \<1000/microliter; patients \> 55 years and \</= 75 years need to be in morphologic remission at transplant (\< 5% blasts). 5. Myelodysplastic syndrome (MDS) with International Prognostic Scoring System (IPSS) intermediate-2 or higher; or therapy-related MDS 6. Aplastic anemia with Absolute neutrophil count (ANC)\<1000 and transfusion dependent after they failed immunosuppression therapy 7. Chronic myeloid leukemia (CML) \>/=1st chronic phase, after failed \>/=2 lines of tyrosine kinase inhibitors; in accelerated or blast phase with \> 30% bone marrow blasts; 8. Prior allogeneic stem cell transplant more than 6 months from the first transplant, in remission. 9. Chemotherapy-sensitive relapsed lymphoma (Complete or partial response), Hodgkin's or non-Hodgkin's lymphoma, no evidence of "bulky" disease (\> 10 cm in diameter); 10. Patients with chemo-sensitive CLL with persistent or recurrent disease after fludarabine-based regimens, no evidence of "bulky" disease (\> 10 cm in diameter) 11. Patients with poor prognosis multiple myeloma by cytogenetics (del13, del 17p, t(1;14) or t(14;16) or hypodiploidy, with advanced disease (stage\>/=2) and /or relapsed after autologous stem cell transplant. 12. Patients with myelofibrosis (Lille \>0, transfusion dependency, progression to blast phase; however, in remission from AML) or chronic myelomonocytic leukemia (CMML). These patients will be treated with the reduced-intensity conditioning regimen #2 and will be subject to the same stopping rule as the group \>/= 55 years or with comorbidities. 13. Zubrod performance status 0-1 or Lansky PS greater or equal to 70%. 14. Patients above \>/=65 years old should have an age-adjusted co-morbidity index of \</= 3. 15. Available donor able to undergo a bone marrow harvest. For matched unrelated donor transplants only: Peripheral blood stem cells may be collected if donor is unavailable for bone marrow harvest or if adequate bone marrow cannot be collected. 16. Bilirubin \</= 1.5 mg/dl (unless Gilbert's syndrome), ALT or AST \</= 200 IU/ml. 17. Serum creatinine clearance \>/=50 ml/min (calculated with Cockcroft-Gault formula); Creatinine for children \</=1.5 mg/dl or \</=2 times upper limit of normal for age (whichever is less); 18. Diffusing capacity for carbon monoxide (DLCO) \>/= 45% predicted corrected for hemoglobin. For pediatric patients, if unable to perform pulmonary function, \>/= 92% oxygen saturation with pulse oximetry. 19. Left ventricular ejection fraction (LVEF) \>/= 40%. 20. Patient or patient's legal representative, parent(s) or guardian should provide written informed consent. Assent of a minor if participant's age is at least seven and less than eighteen years. Exclusion Criteria: 1. HIV positive; active hepatitis B or C 2. Patients with active infections. The PI is the final arbiter of the eligibility. 3. Liver cirrhosis with greater than grade 1 stage 1 inflammation/fibrosis 4. Uncontrolled central nervous system (CNS) involvement by tumor cells 5. Patients with AML must have less than 30% bone marrow blasts and no peripheral blood blasts. 6. History of another primary malignancy that has not been in remission for at least 3 years. (The following are exempt from the 3-year limit: non-invasive nonmelanoma skin cancer, fully excised melanoma in situ \[Stage 0\], curatively treated localized prostate cancer, and cervical carcinoma in situ on biopsy or a squamous intraepithelial lesion on PAP smear.) 7. Positive Beta human chorionic gonadotropin (HCG) test in a woman with child bearing potential defined as not post-menopausal for 12 months or no previous surgical sterilization. 8. Inability to comply with medical therapy or follow-up.