Rituximab in Treating Patients Undergoing Donor Peripheral Blood Stem Cell Transplant for Relapsed or Refractory B-cell Lymphoma

This phase II trial studies giving rituximab before and after a donor peripheral blood stem cell transplant in patients with B-cell lymphoma that does not respond to treatment (refractory) or has come back after a period of improvement (relapsed). Monoclonal antibodies, such as rituximab, can interfere with the ability of cancer cells to grow and spread. Giving rituximab before and after a donor peripheral blood stem cell transplant may help stop cancer from coming back and may help keep the patient’s immune system from rejecting the donor’s stem cells.