Prior history of allogeneic stem cell transplantation Must be ineligible for high dose therapy/ stem cell transplantation Prior allogeneic stem-cell transplantation (SCT) Patients with history of allogeneic stem cell transplantation Subjects for whom there is the prospect of stem cell transplantation in the next months in the treatment plan are excluded (including subjects for whom the PdC regimen is being considered as pre-transplant cytoreduction) Has failed to respond to, relapsed following, not eligible for, or opted not to participate in allogeneic stem cell transplantation Suitable candidate to receive allogeneic stem cell transplantation; patient is eligible for study if a suitable candidate refuses to undergo an allogeneic stem cell transplant or a suitable donor cannot be found Patients who are candidates for allogeneic stem cell transplantation. Other high-risk hematologic malignancies eligible for stem cell transplantation per institutional standard 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). Receipt of any organ transplantation, including allogeneic stem-cell transplantation, except of transplants that do not require immunosuppression (e.g., corneal transplant, hair transplant) Patients with history of allogeneic stem cell transplantation are eligible if at least days post-transplant, if there is no evidence of active GVHD and no longer taking immunosuppressive agents for at least days prior to enrollment Prior 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). Patients who in the opinion of the treating physician are unlikely to comply with the restrictions of allogeneic stem cell transplantation based on formal psychosocial screening Relapse after allogeneic stem cell transplantation prior to post-transplant day 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) Is eligible for intensive chemotherapy and/or allogeneic stem cell transplantation. The reason a participant is not eligible for intensive chemotherapy and/or allogeneic stem cell transplantation may consist of one or more of the following factors: Has a history of allogeneic stem cell transplantation Has a history of allogeneic stem cell transplantation Prior stem cell transplantation for myeloma Prior history of stem cell transplantation Prior allogeneic stem cell transplantation (ASCT) or other anti-CD immunotherapy within =< months before first dose of study treatment Prior stem cell transplantation Have undergone allogeneic stem cell transplantation No plan for allogeneic stem cell transplantation within months Patients who have undergone allogeneic stem cell transplantation and have required systemic treatment for GVHD (including but not limited to oral or parenteral corticosteroids, ibrutinib, and extracorporeal phototherapy) within the last weeks Patients who have received prior stem cell transplantation will be allowed to enroll as long as prior transplantation has been at least months before enrollment in the trial and any transplant related toxicities have subsided to grade or less Subjects must not have undergone allogeneic stem cell transplantation Prior treatment with allogeneic stem cell transplantation Has undergone prior allogeneic hematopoetic stem cell transplantation within the last years Patients who have undergone allogeneic stem cell transplantation Patients with B-lineage ALL at least marrow CR in Salvage and beyond with molecular failure at any time point after month of salvage therapy are allowed, including patients who received prior allogeneic stem cell transplantation Patients who have poor or no graft function post stem cell transplantation Allogeneic stem cell transplantation within months, or has active GVHD requiring ongoing immunosuppression. Prior allogeneic stem cell transplantation Patients with B-cell hematological malignancies who are eligible for allogeneic transplantation Prior allogeneic marrow or stem cell transplantation. Minimum donor and stem cell requirements for high-risk patients undergoing stem cell transplantation: Patients with prior stem cell transplants. Patients who have received prior allogeneic stem cell-transplantation Patients who have undergone a stem cell transplantation. Patients who have had a prior stem cell transplantation are NOT eligible for participation No / matched sibling donor available or not financially eligible for allogeneic stem cell transplantation Stem cell transplantation Patients who have received prior stem cell transplantation will be allowed to enroll as long as prior transplantation has been at least months before enrollment in the trial and any transplant related toxicities have subsided to grade or less Have received or are ineligible for immediate established curative regimens, including stem cell transplantation History of allogeneic stem cell transplantation Prior allogeneic stem cell transplantation Patients will have completed induction therapy, achieved st CR and will have completed any planned post-remission therapy; patients are not candidates for allogeneic stem cell transplantation; for purposes of this study, patients who are not candidates for allogeneic stem cell transplantation shall be defined as ) those who do not meet the eligibility criteria of an open allogeneic transplant protocol or ) those who do not have a suitable available human leukocyte antigen (HLA) matched donor available or ) those who refuse to undergo stem cell transplantation or ) those patients whose disease is characterized by \good risk\ features (for AML the following cytogenetic subtypes: t(;), inv(), or t(;), t(;), normal karyotype with mutated nucleophosmin (NPM) and negative for tandem duplication of fms-related tyrosine kinase (FLT-); for ALL: T cell phenotype of any B lineage disease exclusive of t(;) or t(;) in whom allogenic stem cell transplantation in st CR would not be offered as standard of care\r\n* Alternatively, those patients greater than or equal to years of age who have achieved st CR and in whom no further postremission chemotherapy is planned may be enrolled Prior allogeneic stem cell transplantation Prior allogeneic stem cell transplantation (SCT) within the last years. Has undergone prior allogeneic hematopoetic stem cell transplantation within the last years. Prior allogeneic stem-cell transplantation is excluded. Patients deemed clinically eligible for allogeneic stem cell transplantation. Participant must be ineligible or unwilling to undergo stem cell transplantation at time of study entry Inability to comply with the requirements for care after allogeneic stem cell transplantation Prior allogeneic stem-cell transplantation (SCT) Prior allogeneic stem cell transplantation (SCT) Prior allogeneic stem cell transplantation Patients that have received prior allogeneic stem cell transplantation are excluded from this study 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) Diagnosed with AML and eligible for standard induction chemotherapy or stem cell transplantation AML participants < years old must be in second or further relapse or relapsing after allogeneic stem cell transplantation regardless of number of relapses Prior treatment with stem cell transplantation Participants who are newly diagnosed and not considered candidate for high-dose chemotherapy with stem cell transplantation (SCT) due to: being age >= years, or in participants < years: presence of important comorbid conditions likely to have a negative impact on tolerability of high dose chemotherapy with stem cell transplantation Allogeneic stem cell transplantation Prior allogeneic stem cell transplantation Patients must be between - days after allogeneic stem cell transplantation Patients who are immediate candidates for allogeneic bone marrow or stem cell transplantation; patients who refuse this option remain eligible and need to be documented as such in patient medical record Patient who has undergone allogeneic stem cell transplantation Phase I: Patients with diagnosis of multiple myeloma at any stage of disease undergoing high dose chemotherapy and stem cell transplantation; Phase II: Patients with myeloma undergoing a first high dose chemotherapy and stem cell transplantation after achieving at least stable disease following induction therapy; any induction regimen prior to transplantation is allowed; no more than prior lines of therapy prior to transplantation are allowed Subjects must be relapsed/refractory. Prior stem cell transplantation is allowed. History of allogeneic stem cell transplantation Subjects with AML in their first relapse following a remission > months in duration who are eligible for standard therapies (e.g. chemotherapy or stem cell transplantation); Previous hematopoetic stem cell transplantation. Patients must meet institutional criteria for eligibility for non-myeloablative allogeneic stem cell transplantation There are no liver function test criteria for non-myeloablative allogeneic stem cell transplantation Subjects with hematologic malignancies for whom allogeneic stem cell transplantation is deemed clinically appropriate. At the time of registration, stem cell transplantation is not planned within the next months Previous allogeneic stem-cell transplantation Prior history allogeneic stem cell transplantation History of allogeneic stem cell transplantation History of allogeneic stem cell transplantation Prior allogeneic stem cell transplantation Relapse after allogeneic stem cell transplantation prior to post-transplant day Not a candidate for allogeneic stem cell transplantation Patients who have received allogeneic stem cell transplantation < months prior to entering the study Allogeneic stem cell transplantation Prior allogeneic stem cell transplantation. Previous allogeneic stem cell transplantation. The patient has received, or is receiving, allogeneic Stem Cell Transplantation (SCT). The patient has received, or is receiving induction chemotherapy followed by Stem Cell Transplantation. The patient declines to undergo stem cell transplantation or Stem cell transplantation is not available to the patient due to cost or other reasons Prior allogeneic marrow or stem cell transplantation All patients must have a histologic or cytological diagnosis of ALL treated with stem cell transplantation; there are no restrictions on prior therapy Not eligible for stem cell transplantation Stem cell transplantation within preceding days prior to registration Subject underwent allogeneic stem cell transplantation at least months prior to enrollment Patients who have undergone either ablative or non-myeloablative allogeneic stem cell transplantation are eligible Allogeneic stem cell transplantation using in vivo or ex vivo T cell depletion, either by cell manipulation or with T cell depleting antibodies (any anti-thymocyte globulin preparation or alemtuzumab given within days of transplantation) Patients must otherwise fulfill institutional criteria for eligibility to undergo myeloablative allogeneic stem cell transplantation Patients who have undergone allogeneic stem cell transplantation for the treatment of any hematological malignancy are eligible Patients who have had stem-cell transplantation Prior stem cell transplantation Eligible for haploidentical stem cell transplantation according to the investigator Patients with history of allogeneic stem cell transplantation History of allogeneic stem cell transplantation Prior intensive chemotherapy or stem cell transplantation for the treatment of myelodysplastic syndrome