Prior liver transplant History of liver transplant Considered a potential transplant candidate; the attending/treating physician will determine transplant candidacy at the time of consent History of major organ transplant (i.e., heart, lungs, liver, or kidney). Relapse of the underlying cancer or post-transplant lymphoproliferative disease at the time of screening. Liver transplant A diagnosis of post-transplant lymphoproliferative disease (PTLD) Residual disease at the time of transplant (bulky or minimal) or post transplant relapse as evidenced by polymerase chain reaction (PCR) positivity, specific cytogenetic abnormalities, an abnormal population on flow cytometry or increased blasts on bone marrow biopsy or in the peripheral blood; minimal residual disease (MRD) will be defined as detection in blood or marrow of any of the following:\r\n* Any leukemia specific marker (such as t(9:22) or t(4:11)) documented in the patient’s leukemia cells pre transplant on a post transplant evaluation\r\n* An immune globulin rearrangement known to be a disease marker for this patient post transplant\r\n* A leukemia specific phenotype post transplant at a level of ? 0.01%\r\n* Mixed donor chimerism (any level) Prior liver transplant The patient must be approved for transplant by the treating transplant physician. This includes completion of their pre-transplant workup, as directed by standard Dartmouth Hitchcock Medical Center (DHMC) standard operating procedures (SOPs) (DHMC SOP – Pre-transplant Evaluation of Allogeneic Recipient). Transaminases < 3 x normal at the time of transplant. Measurable disease of multiple myeloma at the time specified by one of the following:\r\n* If no relapse prior to transplant, values obtained at the time of diagnosis\r\n* If disease relapse prior to transplant and the patient did not have treatment for the relapsed disease prior to transplant, the values obtained at the time of relapse immediately prior to the transplant. \r\n* If disease relapse prior to transplant and the patient did have treatment for the relapsed disease prior to transplant, the values obtained prior to this therapy, ie, the time of relapse Any diagnosis without prior immunosuppressive chemotherapy within 3 months of intended admission for transplant. History of renal or liver transplant Patients who are transplanted at non-US transplant centers Patient may not have received definitive salvage therapy for their post-transplant relapse; use of hydroxyurea is permitted Any prior or planned organ transplant (e.g. liver transplant) Use of two forms of contraception with less than a 5% failure rate or abstinence by all transplanted patients for a minimum of 1 month after the last dose of Idelalisib; for the first 60 days post?transplant, transplant recipients should be encouraged to use non?hormonal contraceptives due to the potential adverse effect of hormones on bone marrow engraftment Eligible for any higher priority transplant protocols Patients must be at least 90 days post-transplant Treatment plan that includes post-transplant maintenance therapy Both transplant and non-transplant candidates are eligible The patient must be approved for transplant by the treating transplant physician. This includes completion of their pre-transplant workup, as directed by standard Dartmouth Hitchcock Medical Center (DHMC) standard of procedure (SOP)s (DHMC SOP – Pre-transplant Evaluation of allogeneic recipient) Transaminases < 3 x normal at the time of transplant Patients with prior transplant of any kind are not eligible Considered transplant-eligible, as determined by the opinion of the investigator at the participating institution; the participating institution does not need to be a transplant center but patients can be referred to a transplant center if needed Participants who are less than 100 days post-transplant, or greater than 100 days post-transplant with active graft versus host disease (GVHD), or are still continuing post-transplant immunosuppressant therapy within 7 days prior to the first dose of study drug. Time to initiation of maintenance therapy: patients may start maintenance therapy as early as 60 days post-transplant and up to 210 days post-transplant; as long as they meet the following criteria: Post-transplant bone marrow blast count ? 5% confirmed by standard of care bone marrow biopsy performed post-transplant (at least 30 days post-transplant). Liver transplant. Prior TACE, radiofrequency ablation (RFA), or liver transplant Must not have myelofibrosis or other disease known to prolong neutrophil engraftment to > 28 days after transplant Prior transplant within 100 days Patients are eligible to start on this protocol if they are between 6 months to 10 months post transplant Pregnant or lactating; women should not breast feed during the interval from study entry to one\r\nyear post-transplant Bone marrow comprising of < 10% lymphoma on most recent biopsy/aspiration (within 9 months of Allo transplant; may have been performed prior to autologous transplant) Additional Eligibility Prior to Transplant Two: Transplant able to occur between day +30 and day +90 from transplant one Relapsed or progressive malignancy after transplant, post-transplant lymphoproliferative disease or any secondary malignancy diagnosed after HCT Must be transplant ineligible as determined by their physician, or if transplant eligible, not expect to undergo transplant for at least 24 months after study enrollment. • Stem cell harvest and mobilization regimen is acceptable if clinically indicated, but must first be confirmed by the Takeda Medical Monitor. Patients who receive post-transplant high dose cyclophosphamide received the transplant < 6 months prior to study Day 1 Prior liver transplant NOTE: Patients proceeding to transplant are allowed up to one cycle of consolidation treatment Planned radiation therapy after transplant Transplant < 4 months prior to study enrollment Subjects with multiple myeloma (MM), Hodgkin’s disease (HD) and non-Hodgkin’s lymphoma (NHL) who are considered eligible for high-dose chemotherapy and autologous PBSC transplant by the transplant team at Kansas University Cancer Center (KUCC); subjects should be enrolled within 30 days of transplant Relapse must have occurred >= 60 days after transplant All patients must have a psychosocial evaluation prior to transplant as per COH SOP FOR COHORT A ONLY: high-dose chemotherapy and AHCT must be planned; post-transplant maintenance therapy will not be permitted Living donor liver transplant (LDLT) Active or recent (within 7 days) episode of transplant associated microangiopathy. Patients unlikely to be available for evaluation at the transplant center on Day 28 and 56 of therapy. Prior liver transplant Have had a liver transplant. Subject is likely to be considered for allogeneic transplant in the opinion of the transplant physician (based on age of patient, health, cytogenetics, and/or molecular characteristics) High-risk AML for which transplant is recommend based on cytogenetic, molecular and morphologic features; patients must meet institutional standards for disease control prior to transplant Subject has had a liver transplant Patients may have had autologous transplant; they must be at least 100 days post transplant, and have had recovery of their counts with absolute neutrophil count (ANC) > 1000 and platelets greater than 100 K at some point post-transplant, and be without active cytomegalovirus (CMV) or fungal disease Patients who have had a prior transplant Started screening no earlier than 75 days after transplant, completed screening within 15 days, and randomized no later than 115 days after transplant. The patient must be approved for transplant by the treating Transplant physician; this includes completion of their pre-transplant workup, as directed by standard DHMC SOPs Severely immunocompromised patients (eg transplant, on immunosuppressive drugs) Participants must not have had a prior transplant ELIGIBILITY TO RECEIVE DLI POST-TRANSPLANT: Time to initiation of maintenance therapy; patients may start maintenance therapy as early as 60 days post-transplant and up to 180 days post-transplant; as long as they meet the following criteria: Lack of care-giver for the early (100-day) post-transplant period Transplant < 60 days prior to study enrollment TRANSPLANT RECIPIENT If patients are found to not be in remission at screening, then the patient may be returned to their primary hematologist/oncologist or may receive chemotherapy as per standard of care for the malignant disease; patients for whom this would be their first allogeneic transplant must be in remission (< 5% malignant blasts in marrow and peripheral blood and no evidence of extramedullary disease) for transplant; patients enrolled on this protocol for their second transplant do not need to have attained remission prior to transplant TRANSPLANT RECIPIENT: 18F FLT CANDIDATE TRANSPLANT RECIPIENT: Meets criteria for transplant recipients History of liver transplant requiring increased immunosuppressive therapy. (Participants on maintenance immunosuppressive therapy after liver transplant are eligible for Part A & B) PRIOR TO POST-TRANSPLANT IMMUNOTHERAPY: Resolution of all transplant related grade III-IV toxicity PRIOR TO POST-TRANSPLANT IMMUNOTHERAPY: WBC >= 2.0 X 10^3/uL PRIOR TO POST-TRANSPLANT IMMUNOTHERAPY (COHORT 2): Able to produce at least 2 doses of fusion vaccine to be considered evaluable; patients who are unable to produce at least 2 doses of fusion vaccine, but otherwise meet eligibility criteria for post-transplant immunotherapy, will be treated with pidilizumab (MDV9300) alone and will be replaced Patient may be enrolled 40 to 100 days after transplant MRD will be defined as detection in blood or marrow of:\r\n* Any leukemia specific marker (such as t[9:22] or t[4:11]) documented in the patient’s leukemia cells pre transplant on a post-transplant evaluation\r\n* A T-cell receptor (TCR) or immune globulin rearrangement known to be a disease marker for this patient post-transplant\r\n* A leukemia specific phenotype post-transplant at a level of >= 0.01%\r\n* Mixed donor chimerism; OR\r\n* With no evidence of ALL or CLL/NHL post-HSCT (to be included in the phase II extension) TIER I SUBJECTS: Patients who have had an autologous transplant must wait at least 180 days from day 0 of autologous transplant to be eligible; patients do not have to relapse following transplant to be eligible provided they meet the 180 day wait post day 0 of transplant requirement; transplant date is defined as the day of infusion of stem cells Must be transplant-eligible per institution guidelines Transplant within 8 weeks Patients wanting to pursue transplant Prior autologous transplant for the disease for which the UCB transplant is being performed. Relapsed within three months post-transplant Patients cannot be on a transplant list Post-transplant lymphoproliferative disorder History of the following therapies in the post-transplant period: Transplant was more than (>) 100 days prior to study enrollment History of liver transplant. Ejection fraction equal or > 50% before admission for transplant as per institutional standards; patients with coronary heart disease (recent myocardial infarctions, angina, cardiac stent, or bypass surgery in the last 6 months or arrhythmia) need to be cleared by cardiology as per Emory bone marrow transplant (BMT) standards Enrollment on any other transplant related protocols Recent salvage transplant (=< 6 months but >= 45 days post-transplant prior to study enrollment) for relapse History of liver transplant Had a prior liver transplant or is planned to undergo liver transplant during the study period; Four months post liver transplant The transplant occurred > 6 months ago Transplant ineligibility History of liver transplant Have a history of major organ transplant (for example: heart, lungs, liver, and kidney) Patients will be eligible to enter the study between 60-120 days post-transplant Patients who have undergone any prior transplant Patients who have previously received an autologous SCT, are excluded if less than 90 days have elapsed from the time of transplant or the patient has not recovered from transplant-associated toxicities prior to the first scheduled dose of MEDI7247. Has undergone a liver transplant, kidney transplant or nephrectomy. Has undergone a liver transplant, kidney transplant or nephrectomy. POST-TRANSPLANT STATUS Liver transplant. Patients must have a pre-transplant multi-organ assessment with the following outcome: Patients who have received their transplant at a different transplant center will not be eligible for the study Prior liver transplant 3-24 months post-transplant (any number of transplant) Children are not eligible as the transplant program is certified as an adult only transplant program Received post-transplant cyclophosphamide Imaging results from within 30 days prior to transplant (used as baseline measure for documentation of disease status); results may be obtained at a time point greater than 30 days from transplant if obtained per the patient’s standard of care and with prior sponsor approval Prior liver transplant Patients must have undergone an autologous transplant =< 12 months prior to transplant on this study or have received multi-agent or immunosuppressive chemotherapy within 3 months of the preparative regimen Subject who is scheduled to have a cord blood transplant or a haploidentical transplant Patients receiving T cell depletion or thymoglobulin as part of their transplant Prior liver transplant Have anticipated in-patient status for 14 to 20 days from the time of transplant.