CD45RA-depleted CD19-CAR T Cell Consolidation After TCRαβ+/CD19 B Cell-depleted Haploidentical Hematopoietic Cell Transplantation for Relapsed/Refractory CD19+ ALL and Lymphoma

The purpose of this study is to learn more about newer methods of transplanting blood cells donated by a partially matched family member to children with high-risk CD19 positive leukemia ALL. Primary Objective: \- To assess the safety and feasibility of combining CD19-CAR(Mem) T cells after TCRαβ+/CD19 depleted haploidentical donor transplantation for pediatric patients with relapsed/refractory CD19+ B-cell malignancies. Secondary Objectives: * To estimate 1-year post-transplant overall survival, event-free survival, and GVHD-free relapse-free survival (GRFS). * To estimate cumulative incidence of engraftment, acute and chronic GVHD, and immune-related adverse events, including CRS and ICANS.

This is a Phase I study evaluating the addback of CD19-CAR(Mem) T cells after TCRαβ+/CD19 B cell depleted haploidentical donor transplantation for pediatric patients with relapsed/refractory CD19+ B-cell malignancies. Donors that meet eligibility criteria will be consented to undergo two separate collections: 1) G-CSF mobilized stem cell graft via apheresis for progenitor cell infusion and 2) Non-mobilized peripheral blood mononuclear cells (PBMC) via apheresis for subsequent CAR T-cell manufacturing and DLI if needed. Patients that meet eligibility criteria to receive therapy will be consented to proceed on study. Treatment will include a conditioning chemotherapy preparative regimen followed by infusion of TCRαβ/CD19 B cell depleted progenitor cell infusion on day 0. Then as early as day + 14 patients will receive the previously manufactured CD19-CAR(Mem) T cell product. Patients will then be monitored for safety and efficacy of the infused CAR T-cell product, as well as collection of correlative samples.