Has had an allogeneic tissue/solid organ transplant. Prior allogeneic stem cell transplant or solid organ transplant History of allogeneic bone marrow, stem-cell, or solid organ transplant Prior allogeneic bone marrow or solid organ transplant Has had an allogeneic tissue/solid organ transplant, prior stem cell or bone marrow transplant Any prior allogeneic hematopoietic stem cell or solid organ transplant. Patients are not eligible if they have had or are planned for solid organ transplant or allogeneic hematopoietic stem cell transplant Had a solid organ or allogeneic bone marrow transplant Has had an allogeneic tissue/solid organ transplant Previously received a solid organ transplant or allogeneic progenitor/stem cell transplant. Prior allogeneic stem cell or solid organ transplant Prior allogeneic stem cell or solid organ transplant Prior allogeneic stem cell or solid organ transplant; Solid organ or tissue transplant including stem cell transplant Prior allogeneic transplant of any solid organ or bone marrow/stem cells Has had an allogeneic tissue/solid organ transplant. Prior allogeneic stem cell or solid organ transplant Prior allogeneic stem cell or solid organ transplant History of allogeneic tissue or solid organ transplant History of allogeneic tissue/solid organ transplant, prior stem cell or bone marrow transplant. Prior allogeneic stem cell transplant or solid organ transplant Received a stem cell transplant for Hodgkin Lymphoma and/or a solid organ transplant Has had an allogeneic tissue/solid organ transplant Prior allogeneic solid organ transplant Patient with history of prior solid organ or allogeneic bone marrow transplant Patients who have a history of an allogeneic tissue/solid organ transplant are not eligible Has had an allogeneic tissue/solid organ transplant History of solid organ or stem cell transplant requiring immunosuppressive medications History of solid organ or stem cell transplant requiring immunosuppressive medications Prior allogeneic stem cell transplant or solid organ transplant Prior allogeneic stem cell or solid organ transplant Prior allogeneic stem cell transplant or solid organ transplant Prior allogeneic stem cell or solid organ transplant Prior allogeneic bone marrow or solid organ transplant History of allogeneic tissue/solid organ transplant Prior allogeneic stem cell or solid organ transplant History of allogeneic bone marrow, stem cell, or solid organ transplant Has had an allogeneic tissue/solid organ transplant Prior allogeneic stem cell or solid organ transplant Prior allogeneic stem cell or solid organ transplant Has had previous allogeneic tissue/solid organ transplant History of allogeneic bone marrow, stem cell, or solid organ transplant Prior allotransplant, including allogeneic hematopoietic cell transplant or solid organ allogeneic transplant Prior solid organ or stem cell transplant Prior allogeneic stem cell or solid organ transplant Has previously had a hematopoetic stem cell transplant or solid organ transplant Participants with prior allogeneic stem cell or solid organ transplantation Prior allogeneic stem cell or solid organ transplantation History of allogeneic stem-cell (or other organ) transplantation Prior allogeneic stem cell or solid organ transplantation; Prior allogeneic stem cell or solid organ transplantation Prior allogeneic stem cell or solid organ transplantation History of solid organ or stem cell transplantation Prior allogeneic stem cell or solid organ transplantation. Prior allogeneic stem cell or solid organ transplantation Prior allogeneic stem cell or solid organ transplantation Receipt of any organ transplantation including autologous or allogeneic stem-cell transplantation. Prior allogeneic stem cell or solid organ transplantation Prior allogenic stem cell or solid organ transplantation Patients with prior allogeneic stem cell or solid organ transplantation. Receipt of any organ transplantation including allogeneic stem-cell transplantation. Receipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant). History of organ transplantation (e.g. stem cell or solid organ transplant) Receipt of any organ transplantation, including allogeneic stem-cell transplantation, except of transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant) Prior allogeneic stem cell or solid organ transplantation For cohort 1 (DLBCL) only: prior organ transplantation including allogeneic stem-cell transplantation Receipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant). Has undergone solid organ transplant at any time, or prior allogeneic hematopoietic stem cell transplantation within the last 5 years Prior allogeneic stem cell or solid organ transplantation Prior allogeneic stem cell or solid organ transplantation Prior organ transplantation, including allogeneic stem cell transplantation Prior allogeneic stem cell or organ transplantation including corneal transplant Prior allogeneic stem cell or solid organ transplantation Receipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (e.g. corneal transplant, hair transplant) History of solid organ or stem cell transplantation Prior organ transplantation including allogeneic stem cell transplantation, brain metastases (except those meeting certain protocol specified criteria which are acceptable), significant acute or chronic infections, a history of cardiovascular/cerebrovascular disease. History of allogeneic stem?cell (or other organ) transplantation Prior organ transplantation including allogeneic stem cell transplantation Participants with prior allogeneic stem cell or solid organ transplantation Prior organ transplantation including allogeneic stem-cell transplants Prior organ transplantation including allogeneic stem-cell transplantation Prior organ transplantation, including allogeneic stem cell transplantation Prior organ transplantation, including allogeneic stem cell transplantation Patients with a prior history of allogeneic stem cell or solid organ transplantation Receipt of any organ transplantation including allogeneic stem-cell transplantation Patients with prior stem cell transplantation or solid organ transplantation. Patients with prior allogeneic stem cell or solid organ transplantation Have undergone organ transplantation including allogeneic or autologous stem-cell transplantation, at any time; Patients with history of organ and allogeneic stem cell transplantation Previous history of autologous or allogeneic blood stem cell transplantation or solid organ transplantation History of allogeneic stem cell transplantation, prior solid organ transplant, or anticipated to undergo solid organ transplantation, or left ventricular assist device (LVAD) implantation, during the course of the study. Patients with prior stem cell transplantation or solid organ transplantation. Patients with a prior history of allogeneic stem cell or solid organ transplantation Prior allogeneic stem cell or solid organ transplantation Prior stem cell transplantation or solid organ transplantation History of organ or previous autologous/allogeneic stem cell transplantation Prior allogeneic stem cell or solid organ transplantation Prior organ transplantation, including allogeneic stem-cell transplantation Has undergone prior organ or allogeneic hematopoetic stem cell transplantation Prior allogeneic stem cell or solid organ transplantation Subjects has history of organ or allogeneic stem cell transplantation Prior allogeneic stem cell or solid organ transplantation Has undergone prior organ or allogeneic hematopoetic stem cell transplantation Prior allogeneic hematopoietic stem-cell transplantation or prior solid-organ transplantation Prior organ transplantation, including allogeneic stem-cell transplantation Prior allogeneic stem cell or solid organ transplantation History of allogeneic stem cell or solid organ transplantation Receipt of any organ transplantation, including allogeneic stem-cell transplantation, but with the exception of transplants that do not require immunosuppression (eg, corneal transplant, hair transplant) Prior organ transplantation, including allogeneic stem cell transplantation Participants with prior allogeneic stem cell or solid organ transplantation Prior allogeneic hematopoietic stem cell transplantation or solid organ transplantation Receipt of any organ transplantation, including allogeneic stem-cell transplantation. history of allogeneic stem cell or solid organ transplantation. Prior allogeneic stem cell or solid organ transplantation Prior allogeneic stem cell or solid organ transplantation History of myelodysplastic syndrome, allogeneic stem cell or solid organ transplantation History of allogeneic stem-cell (or other organ) transplantation Prior organ transplantation including allogeneic stem-cell transplantation History of prior allogeneic hematopoietic stem cell transplantation or prior solid organ transplantation Prior allogeneic stem cell or solid organ transplantation Prior allogeneic stem cell or solid organ transplantation Patients who have previously received a prior organ transplantation, including allogeneic stem cell transplantation Prior organ transplantation, including allogeneic stem cell transplantation Prior organ transplantation, including allogeneic stem cell transplantation Prior allogeneic stem cell or solid organ transplantation Participants with prior allogeneic stem cell or solid organ transplantation Patients who previously received a solid organ transplant Patients with any history of solid organ or bone marrow transplant will not be eligible Previous HCT or solid organ transplant. Organ transplant recipients other than bone marrow transplant Prior solid organ transplant Patients scheduled for a combined transplant (such as liver-kidney), or having a previous solid organ, bone marrow, or autologous islet cell transplant. Prior solid organ or hematologic transplant. Organ transplant recipients History of major solid organ transplant (i.e., heart, lungs, liver and kidney). EXCLUSION - PROCUREMENT: History of solid organ transplant EXCLUSION - INFUSION: History of solid organ transplant Prior solid organ transplant. Organ transplant History of prior solid organ or bone marrow transplant Prior solid organ transplant M1c disease (solid organ metastasis) Organ transplant recipient Any solid organ transplant or bone marrow transplant Had a solid organ or hematologic transplant. Has had a prior solid organ transplant. Prior organ transplant requiring immunosuppressive therapy. Participants that have had bone marrow or solid organ transplant are excluded. Patients who have undergone a bone marrow or solid organ transplant Had a solid organ or hematologic transplant Subjects who have had solid organ transplant Receipt of solid organ transplant History of allogeneic organ transplant (e.g. solid organ/bone marrow transplant patients) Patients with a history of solid organ transplant Had a solid organ or hematologic transplant Had a solid organ or hematologic transplant Prior solid organ transplant Patients with previous solid organ transplant Malignancy attributed to prior solid organ transplant Prior solid organ transplant requiring immunosuppressive therapy Prior organ transplant requiring immunosuppressive therapy Prior solid organ transplant History of organ transplant requiring therapeutic immunosuppression History of solid organ transplant History of immunodeficiency, solid organ transplant, or tuberculosis Has a history of a bone marrow or solid organ transplant. Previous organ transplant Prior organ transplant requiring immunosuppressive therapy Solid organ transplant Has had a solid organ or hematologic transplant. Has had a prior solid organ transplant. Has had a prior solid organ transplant. Organ transplant recipients other than bone marrow transplant; Other immunocompromised status (e.g. organ transplant) Status post solid organ transplant. Patient has received an organ transplant Had a solid organ or hematologic transplant Undergone a bone marrow or solid organ transplant. Previous organ transplant Prior organ transplant requiring immunosuppressive therapy Subject has received an organ transplant Patients who have previously received a solid organ transplant are not eligible Prior bone marrow transplant or history of organ transplant requiring the need for any chronic immunosuppressive medications Previous organ transplant History of any organ or bone marrow transplant Prior solid organ transplant Planned organ transplant during the study Prior organ transplant requiring immunosuppressive therapy Undergone a liver or other organ transplant Subjects who have received any type of solid organ transplant Patients who have undergone hematopoietic cell transplant (HCT), solid organ transplant (SOT) Patients with known HIV or with solid organ transplant History of solid organ transplant or bone marrow transplant Patients who have received organ transplant Single solid organ recipients (kidney only) Organ transplant recipient History of organ transplant requiring therapeutic immunosuppression Subjects with a previous solid organ transplant History (hx) of organ transplant Organ Transplant: Patients may NOT be the recipients of an organ transplant. GENERAL EXCLUSION CRITERIA FOR SUBPROTOCOLS: Patients who have had a prior solid organ transplant are not eligible Prior organ transplant Received solid organ transplant (kidney or other) Single solid organ recipient (kidney only) Prior solid organ or bone marrow transplant Subjects who have received any type of solid organ transplant Prior organ transplant History of allogenic bone marrow or solid organ transplant Autologous or allogenic transplant within the 60 days prior to Cycle 1 Day 1. Has had an allogenic tissue/sold organ transplant. History of autologous/allogenic bone marrow transplant. Previous allogenic bone marrow transplant. Subjects with a history of autologous or allogenic stem cell transplantation must have adequate peripheral blood counts independent of any growth factor support, and have recovered from any transplant related toxicity(s) and be at least 100 days post-autologous transplant prior to first dose of study drug or at least 6 months post-allogenic transplant prior to first dose of study drug and not have active graft-versus-host disease (GVHD), i.e., requiring treatment. Prior organ transplant including allogenic hematopoietic stem cell transplant Prior allogenic stem cell or solid organ transplant Autologous stem cell transplant within 6 weeks before enrollment or any history of allogenic transplant Prior allogenic transplant Has allogenic haemopoietic stem cell (HSC) transplant. Has had an allogenic tissue/solid organ transplant History of allogenic transplant History of allogenic transplant Autologous or allogenic transplant within the 60 days prior to Screening. Eligible for allogenic or autologous stem cell transplant Patients within 60 days of allogenic bone transplant are not eligible; patients with solid organ transplant are not eligible Autologous or allogenic transplant within the 60 days prior to the Screening visit. Allogenic tissue/solid organ transplant History of allogenic organ transplant. History of an autologous/allogenic bone marrow transplant. Undergone an allogenic stem cell transplant Subjects with a history of autologous or allogenic stem cell transplant must have adequate bone marrow independent of any growth factor support, and have recovered from any transplant related toxicity(s); and either greater than 100 days post-autologous transplant (prior to first dose of study drug) or greater than or equal to 6 months post-allogenic transplant (prior to first dose of study drug) and not have active graft-versus-host disease (i.e., requiring treatment). Have previously received an allogenic stem cell transplant Receipt of allogenic or autologous stem cell transplant More than 2 months out from allogenic hematopoietic stem cell transplant prior to randomization. Previous allogenic hematopoietic transplant within 90 d History of allogenic organ transplant Prior allogenic stem cell or solid organ transplant Has previously received an allogenic hematopoietic stem cell transplant. Prior allogenic stem cell or solid organ transplant Autologous or allogenic transplant within the 60 days prior to Screening. cHL COHORT ONLY: history of allogeneic transplant Previous allogeneic bone marrow transplant Patients with previous allogeneic bone marrow transplant Prior allogeneic transplant Previous allogeneic transplant Subject with a history of organ transplant or allogeneic bone marrow transplant; Prior allogeneic transplant Has received an allogeneic bone marrow or allogeneic stem cell transplant. History of an allogeneic bone marrow transplant. Prior allogeneic bone marrow transplant. Participants who have received a previous allogeneic bone marrow transplant Participant has had a prior allogeneic transplant. Subjects with clinically significant cardiovascular disease, history of organ transplant or allogeneic bone marrow transplant, active known or history of autoimmune disease that might recur or major surgery within 28 days prior to the first dose or still recovering from prior surgery. Participants who are within 6 months of an allogeneic bone marrow transplant the subject has recovered from transplant-associated toxicities prior to the first dose of GSK525762, and For subjects with a prior history of allogeneic transplant, Clinically significant pulmonary dysfunction, active infection, prior allogeneic bone marrow transplant, active autoimmune disease Prior allogeneic transplant if performed < 6 months prior to first dose of AMV564, if patient has active GVHD, or if patient has not been off immunosuppressive Previous allogeneic transplant Prior allogeneic bone marrow transplant within 12 months of screening date Prior allogeneic transplant, within the last 5 years We will exclude patients who are eligible for an allogeneic bone marrow transplant at the time of study enrollment; if an enrolled patient subsequently becomes eligible for transplant, they will not be prevented from proceeding to the appropriate clinical treatment indicated FOR ALL PHASES (Ib AND II): History of having received an allogeneic bone marrow or organ transplant Previous allogeneic bone marrow transplant Prior allogeneic bone marrow transplant Prior allogeneic transplant Prior allogeneic transplant Willingness to have an allogeneic transplant Have undergone a prior allogeneic bone marrow transplant (BMT) PART 1: History of prior allogeneic transplant History of an allogeneic solid organ transplant or bone marrow transplant, or current active immunosuppressive therapy such as cyclosporine, tacrolimus, etc. Allogeneic transplant with a human leukocyte antigen (HLA)-identical sibling will be recommended for patients < 55 years; if the patient refuses allogeneic transplant, they may still be eligible for this protocol Prior allogeneic transplant Patients with secondary AML, and patients with a prior autologous and allogeneic bone marrow transplant are eligible Subject has a history of organ transplant or allogeneic bone marrow transplant; Receipt of an allogeneic bone marrow or allogeneic stem cell transplant Patients who received an allogeneic bone marrow or allogeneic peripheral blood stem cell transplant less than 12 months prior to initiation of study Has a transplanted organ or has undergone allogeneic bone marrow transplant Patients eligible, at the time of starting treatment, for curative therapeutic approaches (such as allogeneic transplant) are not eligible for the trial; however, patients who achieve CR or partial response (PR) as a result of therapy on this trial may proceed to allogeneic transplant Prior allogeneic transplant Prior allogeneic bone marrow transplant Patients with an organ transplant, including those that have received an allogeneic bone marrow transplant. History of having received an allogeneic bone marrow or organ transplant History of an allogeneic solid organ transplant or bone marrow transplant, or current active immunosuppressive therapy such as cyclosporine, tacrolimus, etc. Previous allogeneic bone marrow transplant. Prior allogeneic transplant of any kind Eligible for allogeneic transplant in the treating physicians’ judgment and by institutional standards Previously received an allogeneic transplant Autologous or allogeneic bone marrow transplant as second-line therapy. Prior allogeneic transplant Prior allogeneic transplant > 60 days after reduced intensity conditioning (RIC) allogeneic transplant for lymphoma Prior allogeneic transplant Has received an allogeneic bone marrow or allogeneic stem cell transplant. Eligible for allogeneic bone marrow transplant. Receipt of an allogeneic transplant. No more than 4 prior lines of systemic anti-cancer therapy and no prior bone marrow transplant or stem cell transplant within 12 months of dosing, and no prior allogeneic transplant. Subjects who received an allogeneic bone marrow or allogeneic peripheral blood stem cell transplant Previously received an allogeneic transplant. Any prior allogeneic transplant. Allogeneic transplant recipients undergoing ablative transplants will also be eligible to participate; those receiving nonablative regimens (a small proportion of allogeneic transplant recipients at UWCCC) will be excluded Patients who have failed a prior autologous or allogeneic transplant are eligible; however, at least 6 months must have elapsed between the start of this reduced intensity conditioning regimen and the last transplant if patient had a prior autologous or myeloablative allogeneic bone marrow transplant (BMT) Prior allogeneic transplant Underwent a previous related or unrelated allogeneic transplant Prior allogeneic transplant Prior allogeneic transplant Patients who have received a prior allogeneic transplant will be excluded Subject has had prior allogeneic transplant. Has received an allogeneic transplant in the past; scheduled to receive a second allogeneic transplant Prior allogeneic BMT Prior solid organ or bone marrow progenitor cell transplantation. History of prior allogeneic bone marrow, stem-cell, or solid organ transplantation History of prior allogeneic bone marrow progenitor cell or solid organ transplantation History of prior allogeneic bone marrow, stem-cell or solid organ transplantation. History of prior allogeneic bone marrow progenitor cell or solid organ transplantation History of solid organ, allogeneic bone marrow, or stem cell transplantation within the 6 months prior to consent. History of prior allogeneic bone marrow progenitor cell or solid organ transplantation. History of prior allogeneic bone marrow progenitor cell or solid organ transplantation Prior solid organ or bone marrow progenitor cell transplantation. History of prior allogeneic bone marrow progenitor cell or solid organ transplantation History of prior allogeneic bone marrow progenitor cell or solid organ transplantation History of prior allogeneic bone marrow progenitor cell or solid organ transplantation History of prior allogeneic bone marrow progenitor cell or solid organ transplantation History of solid organ, bone marrow, or progenitor cell transplantation Prior history of allogeneic bone marrow, stem-cell, or solid organ transplantation History of prior allogeneic bone marrow/stem-cell or solid organ transplantation.