Up to 390 mL (78 teaspoons) of blood will be collected from the patient on one to three
      occasions over a two month period. Under certain conditions related to the patient's health,
      the blood may need to be collected using a process called apheresis. Apheresis is the process
      where blood is passed through a machine that separates out the components of the blood that
      is needed. The remainder of the blood is then returned to the patient's body.

      Investigators will use this blood to grow T cells. They will first grow a special type of
      cells called dendritic cells which will cause activity in the T cells. Once these are made
      the investigator will load them with small pieces of protein called peptides taken from the
      TAAs that they want to target. This helps to train the T cells to kill cells with TAAs on
      their surface. Then the investigators expand these TAA-specific CTLs.

      The cells will be infused by intravenous (IV) infusion into the patient over 10 minutes. The
      patient may be pre-treated with acetaminophen (Tylenol) and diphenhydramine (Benadryl).
      Initially, two doses of TAA-specific CTLs will be given two weeks apart. The patient's
      disease will be assessed pre-infusion and then 6 weeks after the second infusion. If after
      the second infusion there is a decrease in the patient's disease or it remains stable, the
      patient can receive up to six (6) additional doses of the TAA-specific CTLs at monthly
      intervals. All of the treatments will be given by the Center for Cell and Gene Therapy at
      Houston Methodist Hospital.

      In between the first and second infusions and for 6 weeks after the last infusion, the
      patient is asked not to receive any other anti-cancer treatments, such as radiation therapy
      or chemotherapy, with the exception of lenalidomide, thalidomide, pomalidomide, or immune
      checkpoint inhibitors, such as CTLA4 and/or PD-1/PD-L1 inhibitors. If they do receive any
      other therapies in-between the first and second infusion of cells, the patient will be taken
      off treatment and will not be able to receive the second infusion of cells.

      This is a dose escalation study. This means that at the beginning, patients will be started
      on the lowest dose (1 of 3 different levels) of TAA-specific CTLs. Once that dose schedule
      proves safe, the next group of patients will be started at a higher dose. This process will
      continue until all 3 dose levels are studied. If the side-effects are too severe, the dose
      will be lowered or the TAA-specific CTL infusions will be stopped.

      Medical Tests Before Treatment

      Before being treated, the patient will receive a series of standard medical tests:

        -  Physical exam.

        -  Blood tests to measure blood cells, kidney and liver function.

        -  Measurement of the patient's multiple myeloma by blood tests and bone marrow biopsy
           (within 4 weeks before the CTL infusion)

        -  Measurements of the patient's tumor by routine imaging studies. We will use the imaging
           study that was used before to follow the patient's tumor: Computerized Tomography (CT),
           Magnetic Resonance Imaging (MRI), or Positron Emission Tomography (PET/CT), skeletal
           bone survey. These studies will be done on a case-by-case basis at the descretion of the
           patient's treating physician.

        -  Pregnancy test (using a blood sample) if the patient is a female who can have children.

      Medical Tests After Treatment:

      Patients will receive standard medical tests after their infusion:

        -  Blood tests to measure blood cells, kidney and liver function.

        -  Measurement of the patient's multiple myeloma by blood tests and bone marrow biopsy (at
           4-6 weeks and 8-12 weeks post 1st CTL infusion).

      To learn more about the way the TAA-specific CTLs are working in the patient's body, an extra
      20-40 mL (4-8 teaspoons) of blood will be taken before each infusion, and at Weeks 1, 2, 4
      and 6. Afterwards, blood will be collected at 3, 6, 9 and 12 months after the last infusion.
      The investigators will use this blood to see how long the TAA-specific CTLs last, and to look
      at the immune response to the cancer. Patients will then be contacted once a year for up to 4
      additional years (total of 5 years follow-up) to evaluate their disease response long-term.