Prior history of allogeneic stem cell transplantation Has a history of having undergone allogeneic stem cell transplantation, or any other allogeneic or xenogeneic transplant Prior allogeneic stem-cell transplantation (SCT) Patients with history of allogeneic stem cell transplantation Patients are considered to have failed available therapies or to be ineligible for or to not be interested in intensive chemotherapies, including allogeneic hematopoietic stem cell transplantation Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. Has ever received or is scheduled to receive an Allogeneic Hematopoietic Stem Cell Transplantation (alloHSCT) 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. Patients who have had an allogeneic hematopoietic stem cell transplantation are not eligible. Has undergone prior allogenic hematopoietic stem cell transplantation. Prior allogenic hematopoietic stem cell transplantation. Relapsed patients who have undergone autologous or allogeneic hematopoietic stem cell transplantation previously Patients with psychological or medical condition that patient's physician deems unacceptable to proceed to allogeneic hematopoietic stem cell transplantation Prior allogeneic stem cell transplantation Prior autologous or allogeneic stem cell transplantation Relapse after allogeneic stem cell transplantation prior to post-transplant day 30 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 Subjects who have opted not to undergo allogeneic hematopoietic stem cell transplantation and who are not deemed eligible for high intensity chemotherapy. Prior history of allogeneic hematopoietic 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-CD22 immunotherapy within =< 4 months before first dose of study treatment Prior autologous or allogeneic stem cell transplantation Must have undergone allogeneic hematopoietic stem cell transplantation (HSCT) (regardless of stem cell source) Prior stem cell transplantation Autologous stem cell transplantation within 12 weeks before the starting IP treatment or past history of allogeneic stem cell transplantation. Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years Previous allogeneic hematopoietic stem cell transplantation Have undergone allogeneic stem cell transplantation No plan for allogeneic stem cell transplantation within 3 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 12 weeks Prior hematopoietic allogenic stem cell transplantation. 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 5 years Patients who have undergone allogeneic stem cell transplantation Patients who have undergone prior autologous stem cell transplantation or allogeneic transplantation Allogeneic stem cell transplantation within 6 months, or has active GVHD requiring ongoing immunosuppression. Prior allogeneic stem cell transplantation Patients with psychological or medical condition that patient's physician deems unacceptable to proceed to allogeneic hematopoietic stem cell transplantation Prior allogeneic marrow or stem cell transplantation. Malignant conditions for which CD34+ selected, T-cell depleted allogeneic hematopoietic stem cell transplantation is indicated such as: Patients eligible for hematopoietic stem cell transplantation 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 Prior allogeneic hematopoietic stem cell transplantation within previous 100 days Stem cell transplantation Patients who have received allogeneic hematopoietic stem cell transplantation are ineligible Previous stem cell collection or transplantation (autologous or allogeneic) History of allogeneic stem cell transplantation Prior allogeneic stem cell transplantation Patients will have completed induction therapy, achieved 1st 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 1) those who do not meet the eligibility criteria of an open allogeneic transplant protocol or 2) those who do not have a suitable available human leukocyte antigen (HLA) matched donor available or 3) those who refuse to undergo stem cell transplantation or 4) those patients whose disease is characterized by \good risk\ features (for AML the following cytogenetic subtypes: t(8;21), inv(16), or t(16;16), t(15;17), normal karyotype with mutated nucleophosmin (NPM1) and negative for tandem duplication of fms-related tyrosine kinase 3 (FLT-3); for ALL: T cell phenotype of any B lineage disease exclusive of t(9;22) or t(4;11) in whom allogenic stem cell transplantation in 1st CR would not be offered as standard of care\r\n* Alternatively, those patients greater than or equal to 60 years of age who have achieved 1st CR and in whom no further postremission chemotherapy is planned may be enrolled Patients who have undergone autologous or allogeneic stem cell transplantation Prior allogeneic stem cell transplantation Prior allogeneic stem cell transplantation (SCT) within the last 5 years. Has undergone prior allogeneic hematopoetic stem cell transplantation within the last 5 years. Allogeneic hematopoietic stem cell transplantation within the last 5 years. Prior allogeneic stem-cell transplantation is excluded. Patients deemed clinically eligible for allogeneic stem cell transplantation. Hematopoietic stem cell transplantation ? 4 months of dosing Inability to comply with the requirements for care after allogeneic stem cell transplantation Patients must NOT have received autologous or allogeneic stem cell transplantation Prior allogeneic stem-cell transplantation (SCT) have undergone previous allogenic stem cell transplantation Prior allogeneic stem cell transplantation (SCT) Has received more than 1 hematopoietic stem cell transplantation. Eligible for allogenic stem cell transplantation. Prior allogeneic stem cell transplantation Patients that have received prior allogeneic stem cell transplantation are excluded from this study Prior stem cell transplantation allogeneic or autologous AML participants < 60 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 Prior stem cell transplantation (autologous or allogeneic) Prior allogeneic hematopoietic stem cell transplantation Prior hematopoietic stem cell transplantation Allogeneic stem cell transplantation Prior allogeneic stem cell transplantation Recipients of prior allogeneic hematopoietic stem cell transplantation Previous allogenic stem cell transplantation. Patients must be between 100 - 200 days after allogeneic stem cell transplantation Patient who has undergone allogeneic stem cell transplantation Day > 100 after allogeneic hematopoietic stem cell transplantation Patients who have undergone prior allogeneic hematopoietic stem cell transplantation History of allogeneic stem cell transplantation Patients who have undergone autologous/allogeneic stem cell transplantation are eligible 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 3 months Prior allogeneic hematopoietic stem cell transplantation (allogeneic stem cell transplant) Previous allogeneic stem-cell transplantation Less than 1 month since completion of autologous stem cell transplantation or less than 3 months since completion of 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 Prior autologous or allogeneic stem cell transplantation Not eligible for an allogeneic hematopoietic stem cell transplantation Relapse after allogeneic stem cell transplantation prior to post-transplant day 30 Not a candidate for allogeneic stem cell transplantation Patients who have received allogeneic stem cell transplantation < 12 months prior to entering the study Allogeneic stem cell transplantation Previous autologous or allogeneic stem cell transplantation. Prior allogeneic stem cell transplantation. Previous allogeneic stem cell transplantation at any time OR autologous stem cell transplantation within 6 months of study entry. Previous allogeneic stem cell transplantation. The patient has received, or is receiving, allogeneic Stem Cell Transplantation (SCT). Prior allogeneic marrow or stem cell transplantation Any patient undergoing allogeneic hematopoietic stem cell transplantation (either 1st or subsequent) Patients who have undergone a prior allogeneic or autologous stem cell transplantation within the previous six months Not eligible for stem cell transplantation Stem cell transplantation within preceding 60 days prior to registration Previous allogeneic hematopoietic stem cell transplantation Subject underwent allogeneic stem cell transplantation at least 6 months prior to enrollment Patients who have undergone either ablative or non-myeloablative allogeneic stem cell transplantation are eligible 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 Prior allogeneic hematopoietic stem cell transplantation Patients who have had stem-cell transplantation Prior stem cell transplantation Prior autologous stem cell transplantation < 1 month or allogeneic stem cell transplantation < 4 months prior to C1D1. Patients must not have had prior stem cell transplantation (autologous or allogeneic) Patients with history of allogeneic stem cell transplantation History of allogeneic stem cell transplantation