Trial of Allogeneic Reduced-Intensity, HLA-Haploidentical Allogeneic Hematopoietic Cell Bone Marrow Transplantation Followed by Graft-versus-Host-Disease (GVHD) Prophylaxis With Cyclophosphamide, Bortezomib and Maraviroc for Hematologic Malignancies ...

* INCLUSION CRITERIA - RECIPIENT: * Participants must have a histologically or cytologically confirmed hematologic malignancy with standard indication for allogeneic hematopoietic cell transplantation including, but not limited to, one of the following: * Acute myeloid leukemia in morphologic complete remission (\<5% blasts in the bone marrow, no detectable abnormal peripheral blasts, and no extramedullary disease) * Any secondary and/or treatment related myeloid neoplasm with antecedent history of myeloid neoplasm or previous chemotherapy/radiation * B-cell acute lymphoblastic leukemia in first or subsequent complete remission * T-cell acute lymphoblastic leukemia in first or subsequent complete remission * Myelodysplastic syndrome of intermediate or higher score by the Revised International Prognostic Scoring System (IPSS-R) * Primary myelofibrosis of intermediate-2 or higher risk by the Dynamic IPSS-Plus (DIPSS-Plus) or high to very high risk score (5 or higher) calculated with MIPSS70+ Calculator; DIPSS-Plus For Myeloproliferative Neoplasms on the Mutation Enhanced International Prognostic Score System (MIPSS70/MIPSS70+) * Chronic myelomonocytic leukemia * Chronic myelogenous leukemia resistant to or intolerant of \>=3 tyrosine kinase inhibitors or with history of accelerated phase or blast crisis * B-cell lymphoma including Hodgkin lymphoma that has relapsed/progressed within 1 year of completion of primary treatment, after autologous transplantation or has progressed through at least 2 lines of therapy * Burkitt or lymphoblastic lymphoma: high-risk disease in first remission, progression/relapse after \>=1 previous regimen * Chronic lymphocytic leukemia with 17p deletion and/or unmutated IgHv or refractory or intolerant of both BTK and PI3K inhibitors * Mature T or NK neoplasms as defined in the WHO guidelines of sufficient type and severity for allogeneic HCT based on published clinical practice guidelines * T-Prolymphocytic leukemia progressing/relapsing after alemtuzumab and at least one other regimen * B-Prolymphocytic leukemia progressing/relapsing after fludarabine and at least one other salvage regimen * Hematologic malignancy of dendritic cell or histiocytic cell type * Multiple myeloma that relapses after therapy with both a proteasome inhibitor and an immunomodulatory drug (IMiD), relapses after autologous transplantation, or manifests as plasma cell leukemia In addition to standard indications for HCT: Participant with a hematologic malignancy eligible for consolidation of first remission with autologous transplantation, if autologous transplantation is not accessible to the participant. * HIV seropositive, with ART regimen that, when stable for \>4 weeks, is associated with an HIV viral load \<400 copies/mL at screening evaluations. Subsequent changes to avoid/optimize drug interactions with study drugs or essential supportive care drugs may be made to the ART regimen at any time during the eligibility assessment period, as long as the eligibility criteria were met and the regimen change is expected, by the study team and involved consultants/pharmacy, to be similarly effective for HIV control. These changes to the ART regimen are not part of the study. If changes to the ART regimen are made during the eligibility period, HIV viral load will be rechecked at least 1 week after the change but prior to protocol treatment consent. * Dose level 1: ART regimen must include maraviroc * Dose level 2 and 3: ART regimen must not include maraviroc and there must be no history of maraviroc intolerance or resistance * Age \>= 18 years * At least one potentially suitable HLA-haploidentical first degree or collateral related donor. Recipients with donor-specific anti-HLA antibodies (DSAs) to all potential donors must have at least one potential donor option where the DSA strength has a mean fluorescence intensity of \< 5000 and antibodies are not complement-fixing. * Karnofsky performance score \>=50 percent. * Adequate organ function defined as possessing all of the following: * Cardiac ejection fraction by 2D ECHO of \>=40 percent * Forced expiratory volume-1 (FEV-1), forced vital capacity (FVC), and diffusing capacity of the lung for carbon monoxide (DLco, adjusted for hemoglobin) all of \>=40 percent predicted. If unable to perform pulmonary function tests, there should be no evidence of dyspnea at rest, no requirement for supplemental oxygen, and oxygen saturation \>92 percent on room air. * Total bilirubin \<=3.0 mg/dL (unless due to Gilbert's or hemolysis), alanine aminotransferase (ALT), and aspartate aminotransferase (AST) \<= 5x the upper limit of normal, gamma glutamyl transferase (GGT) \<= 5x the upper limit of normal * Estimated serum creatinine clearance of \>=50 mL/min/1.73m2 calculated using eGFR in the clinical lab * Ability of participant to understand and the willingness to sign a written informed consent document. * Individuals of childbearing potential and those that can father children must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for at least one-year post-allo HCT. EXCLUSION CRITERIA - RECIPIENT: * Participants who are receiving any other investigational agents that cannot be discontinued/completed at least 2 weeks prior to the date of beginning conditioning. * Poorly controlled malignant indication for transplantation, defined as: * Leukemia not having achieved morphologic remission (i.e. bone marrow blasts \>5 percent or active extramedullary disease) * Lymphoma not having demonstrated some degree of treatment sensitivity (chemosensitivity, radiosensitivity) by clinical and/or radiologic assessment * Multiple myeloma not in complete remission, as determined by negative immunofixation in serum and urine and disappearance of any soft tissue plasmacytomas and \<= 5 percent plasma cells in the bone marrow. * Uncontrolled intercurrent illness that in the opinion of the PI would make it unsafe to proceed with transplantation. * Study team is unable to identify an adequate antiretroviral regimen to adequately suppress the HIV viral load \<400 copies/mL that is compatible with study drugs * Pregnancy * For lactating potential participants: unwilling to discontinue lactation prior to the start of study treatment on day -14. * Prohibitive allergy to a study drug or to compounds of similar chemical or biologic composition of the agents (eATG, steroids, cyclophosphamide, busulfan, pentostatin, maraviroc, bortezomib, plerixafor (dose level 3 only)) used in the study. * Lack of central access potential sufficient for transplant * Active psychiatric disorder which is deemed by the PI to have significant risk of compromising compliance with the transplant protocol and/or antiretroviral therapy * Grade 3-4 motor or sensory neuropathy per CTCAE version 5.0 INCLUSION CRITERIA - RELATED DONOR: * Related donor (age \>=12) deemed suitable and eligible, and willing to donate, per clinical evaluations, who are additionally willing to donate blood and/or PBSC graft aliquotfor research. Related donors will be evaluated in accordance with existing institutional Standard Policies and Procedures for determination of eligibility and suitability for clinical donation. * Ability of participant or parent/legal guardian to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA - RELATED DONOR: -Failure to qualify per institutional Standard Policies