Multiple myeloma is a cancer of the plasma cells. Treatment for myeloma includes stem cell transplantation. The purpose of this project is to study the immune system of patients with multiple myeloma who have undergone a stem cell transplant followed by an infusion of their own T cells. We will also vaccinate these patients using a pneumococcal vaccine at different time points to determine the optimal schedule for vaccination. These studies will lead to a better understanding of immune system recovery after transplantation and how to improve immune responses to myeloma and antimyeloma vaccines.