- Subjects must have stored in usable condition for second ASCT, as judged by the principal investigator, ≥3x106 CD34+ cells per kg of body weight (either autologous or syngeneic) stored in at least two bags such that after administration of the minimum dose of 2 x 106 CD34+ cells/kg required on this protocol that a separate aliquot of at least 1 x 106 CD34+ cells/kg remains for rescue infusion in the event of graft failure. Patients with inadequate stem cells stored may still sign consent and undergo a mobilization/collection procedure either before or after apheresis for T cell harvest. If this is required and is undertaken prior to apheresis for T cell harvest, two weeks must elapse between the last day of stem cell collection and apheresis for T cell harvest.