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 ...

Background: * Human Immunodeficiency Virus (HIV) infection should not be considered a barrier to hematopoietic cell transplantation (HCT) in patients who otherwise have a standard indication for HCT. * The main historical barriers include the risk of opportunistic infections, drug interactions, and lack of donor availability. * This study addresses these barriers by requiring adequate HIV control with anti-retroviral therapies which do not interact with the transplant medications and by utilizing HLA-haploidentical donors. * Cellular reservoirs that harbor latent HIV are cells of hematopoietic origin, and thus HCT is a potential cure for HIV if all hematopoietic/immune cells can convert to fully donors without HIV infection of these cells. * CCR5 receptor and CXCR4 are chemokine co-receptors that enable HIV entry into cells. * Obtaining a CCR5-delta-32 homozygous donor lacks feasibility for the majority of people living with HIV (PLWH) requiring HCT, particularly those of minority ethnic backgrounds. * Agents used to prevent graft-versus-host disease (GVHD) include post-transplantation cyclophosphamide (PTCy), maraviroc, and bortezomib * PTCy expands the donor pool by allowing HLA-mismatched donor HCT with good engraftment and low rates of GVHD. PTCy typically combined with other agents as adjuncts for GVHD prophylaxis, standardly a calcineurin inhibitor and mycophenolate mofetil * Bortezomib has been used in combination with PTCy as GVHD prophylaxis and may additionally inhibit HIV infection of donor cells * Maraviroc is used as GVHD prophylaxis, but not previously in combination with PTCy and bortezomib, and is additionally a CCR5 receptor blocker, which may inhibit HIV infection of donor cells. Maraviroc is an HIV medication used in modern ART regimens. * This protocol is a step-wise evaluation of a GVHD prophylaxis regimen of PTCy and bortezomib in recipients of HLA-haploidentical grafts among those who are on maraviroc, followed by a de-escalation of maraviroc to serve purely as GVHD prophylaxis * Plerixafor is used in HCT to promote hematopoietic recovery, akin to the use of G-CSF, and is also a CXCR4 blocker, which may inhibit HIV infection of donor cells Objective: * To determine a safe and recommended phase II dose level regimen. * To determine whether a PTCy-based GVHD prophylaxis regimen including maraviroc and bortezomib can maintain adequate protection against grades III-IV acute GVHD (aGVHD), evaluated at day +100. Eligibility: * Transplant recipient: age \>= 18 years * Transplant recipient must be HIV seropositive * Transplant recipient must have histologically or cytologically confirmed hematologic malignancy with a standard indication for allogeneic HCT, or hematologic malignancy with a standard indication for autologous transplant without access to autologous transplant * There must be at least one potentially suitable HLA-haploidentical donor. Design: * Open-label, single institution, non-randomized, single arm phase II study * CCR5-delta-32 status will be tested among donor options and homozygous donors will be used, if available * Conditioning will consist of eATG 40 mg/kg/day IV on days -14 and -13, pentostatin 4 mg/m\^2/day IV on days -11 and -7, low-dose cyclophosphamide 5 mg/kg/day orally daily on days -11 through -4; busulfan IV, pharmacokinetically dosed, on days -3 and -2. * Peripheral blood stem cells are the only graft source allowed for this study. * GVHD prophylaxis will consist of PTCy 50 mg/kg/day IV on days plus 3 and plus 4, bortezomib 1.3 mg/m\^2 IV in 2 doses at 6 and 72 hours after graft infusion for all participants. The phase I will include 2 dose levels of de-escalated maraviroc * Dose level 1 - PLWH on a maraviroc-containing ART regimen that starts at least 4 weeks before enrollment and continues at least through day plus100 * Dose level 2 - PLWH not on a maraviroc-containing ART regimen, treated with maraviroc 300 mg orally twice daily starting day -3 and given through day plus 30 purely for GVHD prophylaxis * If successful completion of dose level 2, dose level 3 will substitute plerixafor in lieu of G-CSF to the dose level 2 regimen. Plerixafor will be given subcutaneously at 240 microgram/kg every other day, beginning at day plus 1 after transplant through day plus 21, or longer as clinically indicated, such as until ANC recovery.