Dose Escalation Trial of WT1-specific Donor-derived T Cells Following T-Cell Depleted Allogeneic Hematopoietic Stem Cell Transplantation for Patients With Relapsed/Refractory Multiple Myeloma

The purpose of this study is to test the safety of specialized white cells from the donor at different doses. They are called WT1 sensitized T cells. They have been grown in the lab and are immunized against a protein. The protein is called the Wilms' tumor protein, or WT1. The multiple myeloma cells make and express this protein". The investigators want to learn whether the WT1 sensitized T cells will attach to the protein and kill the myeloma cells. The investigators want to find out what effects, good and/or bad, it has on the patient and multiple myeloma.