T-cell Depleted Hematopoietic Stem Cell Boosts Without Conditioning for Poor Marrow Graft Function Following Allogeneic Hematopoietic Stem Cell Transplantation

Inclusion Criteria: * Patients who are diagnosed with PGF are candidates for this trial. * Patients who underwent transplant at another facility and suffer from PGF will be eligible as well as long as a donor is available. PGF can be primary (no counts recovery after the preparative regimen) or secondary (cytopenia after engraftment has occurred). * Patients with auto-immune cytopenia with auto antibodies to neutrophils or platelets or positive Coombs test that did not respond to immunosuppressive agents within 3 months from initiation of therapy are eligible as well. * Persistent cytopenia requiring growth factors and/or blood products AND evidence of hypocellular BM (\<25%). Persistent cytopenia (at least 4 weeks period) is defined by presence of TWO of the following: 1. ANC \<1.0x10\^9/L without filgrastim support or any ANC value that requires recurrent support by filgrastim (administered at least once a week). 2. Plt\<50x10\^9/L 3. Hb\<8 or PRBC transfusion dependent (once every 2 weeks or more) with reticulocyte count of \< 40x10\^9/L. This criteria for persistent cytopenia and hypocellular bone marrow does not apply to patients with auto-immune cytopenia, ONLY PGF patients * Full donor myeloid chimerism. Patients after T cell depletion transplant can have a significant mixed T cell chimerism and this can affect the testing of marrow chimerism. In this case, the neutrophil chimerism will be used to determine eligibility for this trial. Patients will be excluded if neutrophils are less than 90% donor cells; a higher percentage of host cells could be due to relapse or impending relapse. * Age: pediatrics and adults patients. No age exclusion. * Each patient must be willing to participate as a research subject and must sign an informed consent form. * For infections and end organs related criteria (at time of TCD boost administration) see table in protocol. Exclusion Criteria: Patients will be excluded from the trial if at time of enrollment: * Evidence of relapsed disease by morphologic, cytogenetic or molecular diagnostic tools. * Hypersplenism documented by imaging study (US or CT) * Pregnant women * Patient who underwent TCD boost without counts recovery and are considered for another TCD boost will be treated off protocol.