Has received more than allo-HSCT. ELIGIBILITY CRITERIA - PHASE II (ARM D): Patient may be enrolled with a prior allogeneic hematopoietic stem cell transplant (HSCT) but the transplant date must be at least days before date of enrollment; patient must be off immunosuppression and without active GVHD prior to enrollment if previous HSCT Any HSCT within months prior to signing informed consent Any patient who is eligible for HSCT at the time of study screening Autologous HSCT within six weeks prior to start of AMG treatment. Allogeneic HSCT within three months prior to start of AMG treatment. Prior allogeneic HSCT Prior HDT with autologous HSCT Prior allogeneic HSCT History of prior allogeneic HSCT Participants undergoing active therapy for immune-mediated or infectious colitis upon admission for allogeneic HSCT Autologous HSCT within six weeks prior to start of AMG treatment Allogeneic HSCT within three months prior to start of AMG treatment Matched related HSCT Mismatched related HSCT Patients will be eligible to receive donor-derived multiTAA-specific T cells following any type of allogeneic HSCT as:\r\n* Adjuvant therapy for ALL (group A), or\r\n* Treatment for relapsed/residual ALL disease (group B) Any patient regardless of sex or age with CD+ B-ALL undergoing allogeneic HSCT (Group A) OR any patient regardless of sex or age with CD+ B-CLL or NHL undergoing allogeneic HSCT (Group B) High risk of relapse after HSCT, defined as the presence of minimal residual disease as measured by flow cytometry in the absence of evidence of morphologic disease on a bone marrow biopsy prior to HSCT Patient must be ? year and < years of age at screening and undergoing allogeneic HSCT. Patient has had a prior autologous or allogeneic HSCT. Patients with aggressive NHL must have failed autologous hematopoietic stem cell transplantation (HSCT), or are ineligible or not consenting to autologous HSCT Alemtuzumab treatment within weeks of HSCT admission Anti-thymocyte globulin (ATG) within weeks of HSCT admission Allo-HSCT within days of leukapheresis Previous allo-HSCT of any kind Participants who have received allogeneic HSCT within days prior to randomization At the time of allogeneic HSCT: No sooner than days but no later than days after allogeneic HSCT. Hodgkin lymphoma\r\n* Primary treatment failure ineligible for autologous HSCT\r\n* Relapse/progression after autologous HSCT Have a diagnosis of primary aHUS, persistent HSCT-associated TMA or TTP Patients with any type of autologous or allogeneic HSCT with CMV infection will be included Patients excluded from this protocol are those with high risk hematologic malignancies in remission (and no prior allogeneic HSCT), where allogeneic HSCT is indicated but an appropriately matched HSC source (sibling, unrelated adult or UCB) is available Patients who have received a prior allogeneic HSCT and who have either rejected their grafts or who have become tolerant of their grafts with no active GVHD requiring immunosuppressive therapy Relapsed post-autologous HSCT Has undergone prior allogeneic HSCT: Has received autologous HSCT within weeks prior to start of treatment. Other Exclusion Criteria May Apply. Prior allogeneic HSCT. Has received allogeneic hematopoietic cell transplantation (HSCT) within months of planned infusion of genetically modified T cells; HSCT >= months from CAR-T cell infusion eligible. Has received more than allo-HSCT. Subjects with evidence of relapsed primary disease, or subjects who have been treated for relapse after the allo-HSCT was performed. Prior allogeneic HSCT Prior allogeneic HSCT Less than days for subjects receiving autologous hematologic stem cell transplant (HSCT); or months for subjects receiving allogenic HSCT or either transplant type, if otherwise not fully recovered from HSCT related toxicity. Inadequate recovery from toxicity and/or complications from the prior allo-HSCT. If post allogeneic HSCT, patient must not have less than % donor chimerism in either peripheral blood or bone marrow No previous allogeneic HSCT History of allogeneic HSCT or prior autologous HSCT Alemtuzumab treatment within weeks of HSCT admission The patient has received allogeneic hematopoietic stem cell transplantation (HSCT) ? months or autologous HSCT ? days prior to start of Investigational Product (IP). Recipient of an allogeneic HSCT. Patients less than days post HSCT Any patient regardless of sex or age with CD+ B-acute lymphoblastic leukemia (ALL) undergoing allogeneic HSCT (Group A); OR any patient regardless of sex or age with CD+ B-chronic lymphocytic leukemia (CLL) or non-Hodgkin lymphoma (NHL) undergoing allogeneic HSCT (Group B) Hodgkins lymphoma\r\n* Primary treatment failure ineligible for autologous HSCT; relapse/progression after autologous HSCT Recipient of allo-HSCT but not more than allo-HSCT. Relapse of underlying malignant disease after allo-HSCT. The disease indication for which the participant required HSCT must be in remission Prior allogeneic HSCT Patient has received an HSCT transplant for a solid tumor disease. Patients must have received crenolanib on RELHEM prior to HSCT to continue on to maintenance immediately previous cancer chemotherapy, radiotherapy, or immunotherapy; and eligibility for allogeneic HSCT at the time of enrollment. No prior allogeneic HSCT; and Patients with relapsed disease following a prior HSCT may be enrolled into this study as an alternative to a second HSCT or as a bridge-to-transplant regimen. Patients must have a diagnosis of leukemia/lymphoma undergoing active treatment or following HSCT for any indication. Leukemia/lymphoma will be defined according to the National Cancer Institute Surveillance Epidemiology and End Results Collaborative Staging Manual including those conditions defined as borderline such as myelodysplastic syndromes. All forms of HSCT will be eligible, allogeneic as well as autologous. Previous HSCT procedure (autologous or allogeneic) pregnancy Subjects must be undergoing autologous or allogeneic hematopoietic cell transplant (HSCT) with the BEAM conditioning regimen prior to HSCT HSCT procedure scheduled within two months of consent HSCT CGs: Able to give written informed consent HSCT DYADS: In addition to meeting the inclusion criteria for HSCT patients and HSCT CGs, both parties must provide mutual agreement to participate as a dyad HSCT CGs: Inability to complete role responsibilities hours per day for at least % of time (>= days) HSCT DYADS: Participants must not meet the exclusion criteria for HSCT patients and HSCT CGs HSCT DYADS: Patients or CGs who are participating in this study as individuals Treatment plan including autologous HSCT Any previous autologous HSCT must have occurred at least months prior to start of conditioning No previous allogeneic HSCT Requires voriconazole to prevent or treat invasive fungal infection (IFI) post HSCT Preceding allogeneic HSCT Receipt of an HSCT due to an oncological disease No prior HSCT Patients with prior history of HSCT Undergoing allogeneic HSCT from a related or unrelated donor Patients: Receiving an allogeneic HSCT Undergoing an autologous or reduced intensity conditioning (RIC) allogeneic HSCT Patients included in the study will have a hematologic malignancy (any stage or grade) for which they are undergoing preparation for allogeneic HSCT; participants in the study will be restricted to those undergoing HSCT under reduced-intensity protocols and Patient must be scheduled to undergo allogeneic hematopoietic stem cell transplant (HSCT) (adults or pediatric patients) or autologous HSCT (pediatric patients only) and be at high risk or very high risk of developing veno-occlusive disease (VOD). Patients whom have failed prior attempts at allogeneic HSCT Prior myeloablative allogeneic or autologous HSCT Prior allogeneic HSCT Planned to undergo allo-HSCT Allogeneic HSCT within days of leukapheresis Have had a prior allogeneic HSCT Received a previous allogeneic HSCT (previous autologous HSCT is acceptable) First allogeneic HSCT Other chronic disease unrelated to HSCT that may impact bone metabolism