The purpose of this phase I/II study is to explore the feasibility and safety of this approach, and to seek preliminary evidence of effectiveness, of using high-dose cyclophosphamide (50 mg/kg/day x 4) followed by infusion of autologous PBPC enriched for CD34+ cells (concomitantly depleted of CD3+ cells) for the treatment of patients with refractory AITP. Safety/feasibility parameters to be examined will include the ability to mobilize, harvest and purify sufficient PBPC to yield greater than 2 x 10(6) CD34+ cells/kg; symptomatic acceptability and hematologic toxicities of the mobilization regimen (filgrastim 10 micrograms/kg/day IV); tolerability of the leukapheresis procedure, including the central line placement and maintenance; depth and duration of blood cell nadirs following chemotherapy; peritransplant bleeding episodes and transfusion requirements; episodes of febrile neutropenia, culture-proven infections and antibiotic usage. Effectiveness will be gauged by the rapidity and number of patients to achieve complete remission (platelet count greater than 100,000/mm(3) and partial remission (platelet count greater than 50,000/mm(3) or doubling of the platelet count with resolution of bleeding episodes). Ancillary evidence of therapeutic effect will be sought by examining changes in titers of platelet surface glycoprotein antibodies. In addition, alterations in T-lymphocyte subsets will be examined by flow cytometry. If this treatment approach appears feasible, this study will form the basis for a larger trial to compare alternate treatment approaches.