A Safety Study of Human Cord Blood Derived, Culture-expanded, Natural Killer Cell (PNK-007) Infusion With or Without Subcutaneous Recombinant Human Interleukin-2 (rhIL-2) Following Autologous Stem Cell Transplant for Multiple Myeloma (MM)

This study will find the highest acceptable treatment dose and timing of infusion of cord blood, culture expanded natural killer (NK) cells, a kind of immune cell, in patients with multiple myeloma. The NK cells will be given at varying days post autologous stem cell transplant. rhIL-2 is administered after treatment to help the NK cells expand in the body. The safety of this treatment will be studied and researchers want to learn if NK cells will help in treating multiple myeloma.