The following criteria is provided for health care professionals.

Inclusion Criteria:

1. Subjects with a confirmed diagnosis of relapsed refractory multiple myeloma, melanoma, synovial sarcoma, or myxoid/round cell liposarcoma (MRCL) as follows:
   1. Multiple Myeloma
      1. Subjects must have a confirmed prior diagnosis of active MM as defined by the IMWG criteria.
      2. Subjects must have relapsed or refractory disease after either one of the following:
         1. At least 3 prior regimens, which must have contained an alkylating agent, proteasome inhibitor, and immunomodulatory agent (IMiD) OR
         2. At least 2 prior regimens if "double-refractory" to a proteasome inhibitor and IMiD, defined as progression on or within 60 days of treatment with these agents.
         3. Note: Induction therapy, stem cell transplant, and maintenance therapy, if given sequentially without intervening progression, should be considered as 1 "regimen".
      3. Subjects must be at least 90 days since autologous stem cell transplant, if performed.
      4. Toxicities from prior therapies, with the exception of alopecia or peripheral neuropathy attributable to bortezomib, must have recovered to grade ≤ 2 according to the CTC 4.0 criteria or to the subject's prior baseline.
      5. Subjects must have measurable disease per IMWG criteria on study entry, which must include at least 1 of the following:
         1. Serum M-spike ≥ 0.5 g/dL*
         2. 24 hr urine M-spike ≥ 200mg
         3. Involved serum free light chain (FLC) ≥ 50 mg/L with abnormal ratio
         4. Measurable plasmacytoma on exam or imaging
         5. Bone marrow plasma cells ≥ 20%
         6. Note: Patients with IgA myeloma in whom serum protein electrophoresis is deemed unreliable, due to co-migration of normal serum proteins with the paraprotein in the beta region, may be considered eligible as long as total serum IgA level is elevated above normal range.
   2. Provides written, informed consent.
   3. Subjects ≥ 18 years of age.
   4. ECOG performance status of 0-2.
   5. Documented NY-ESO-1 expression on tumor tissue.
   6. HLA-A*201 positive
   7. Subjects of reproductive potential must agree to use acceptable birth control methods, as described in protocol Section 4.3.
   8. Adequate vital organ function as defined by:
      1. Serum creatinine ≤ 2.5 or estimated creatinine clearance ≥30 ml/min and not dialysis-dependent.
      2. Absolute neutrophil count ≥1000/μl and platelet count ≥50,000/μl (≥30,000/μl if bone marrow plasma cells are ≥50% of cellularity for MM patients).
      3. SGOT ≤ 3x the upper limit of normal and total bilirubin ≤ 2.0 mg/dl (except for patients in whom hyperbilirubinemia is attributed to Gilbert's syndrome).
      4. Left ventricular ejection fraction (LVEF) ≥ 45%. LVEF assessment must have been performed within 8 weeks of enrollment.

Exclusion Criteria:

1. Pregnant or nursing (lactating) women.
2. Have inadequate venous access for or contraindications to leukapheresis.
3. Have any active and uncontrolled infection.
4. Active hepatitis B or hepatitis C
5. HIV infection.
6. Any uncontrolled medical or psychiatric disorder that would preclude participation as outlined.
7. NYHA Class III or IV heart failure (see Section 16), unstable angina, or a history of recent (within 6 months) myocardial infarction or sustained (>30 seconds) ventricular tachyarrhythmias.
8. Received prior gene therapy or gene-modified cellular immunotherapy. Subject may have received, however, non-gene-modified autologous T-cells in association with an anti-myeloma vaccine (e.g., hTERT or MAGEA3) or vaccination against infectious agents (e.g., influenza or pneumococcus) as was performed on our previous studies.
9. Active auto-immune disease, including connective tissue disease, uveitis, sarcoidosis, inflammatory bowel disease, or multiple sclerosis, or have a history of severe (as judged by the principal investigator) autoimmune disease requiring prolonged immunosuppressive therapy.
10. Prior allogeneic stem cell transplant.
11. Prior or active central nervous system (CNS) involvement (e.g. leptomeningeal disease, parenchymal masses) with myeloma. Screening for this (e.g. with lumbar puncture) is not required unless suspicious symptoms or radiographic findings are present. Subjects with calvarial disease that extends intracranially and involves the dura will be excluded, even if CSF is negative for myeloma.