A Study of CD45RA+ Depleted Haploidentical Stem Cell Transplantation in Children With Relapsed or Refractory Solid Tumors and Lymphomas

Twelve participants and 12 donors will be enrolled on this study. Donors will undergo seven days of hematopoietic stem cell (HSC) mobilization followed by two apheresis collections. Each apheresis collection will be processed by the CliniMACS system. DONORS: A mobilization regimen of granulocyte colony stimulating factor (G-CSF) will be used to obtain a peripheral blood stem cell (PBSC) product from the donor. Apheresis will be performed for a minimum of two consecutive days, including one day for each cell product delivered. STUDY PARTICIPANTS: Participants will undergo a two-stage haploidentical cell infusion following myeloablative conditioning. The first cell infusion will be a CD3-depleted product and the second infusion will be a CD45RA-depleted product. Primary Objective: * To determine the feasibility of haploidentical HSCT using two infusions engineered by negative selection on the Miltenyi CliniMACS system- the first by selective depletion of CD3+ cells, followed by a second depleted of CD45RA+ cells, in children with relapsed or refractory solid tumors or lymphomas. Secondary Objectives: * To estimate hematopoietic cell recovery and engraftment rates for the patients. * To estimate infection rates and complications. * To estimate the one-year overall survival (OS) and event-free survival (EFS) for the study patients.