Inclusion criteria:

1. Patients with multiple myeloma with an expression of NY-ESO-1 by immunohistochemistry in the pre-enrollment tumor sample
2. Patients are HLA-A\*02:01positive on HLA typing
3. Patients with relapsed or refractory MM (patients with solitary plasmacytoma are not eligible) who meet the following criteria:

1. \> or = 4 prior lines of therapy (including exposure to at least one proteasome inhibitor, ImiD, and anti-cd38 antibody and bcma targeted agent
2. have measurable disease (serum monoclonal (M) protein level ≥0.5 g/dL, and/or urine M protein level ≥200 mg/day, and/or involved serum FLC level ≥10 mg/dL provided the serum-free light-chain ratio is abnormal \*refractory is defined as a documented progressive disease during or within 60 days \[measured from the last dose of any drug within the regimen\] of completing treatment with the last anti-myeloma regimen before study entry.
4. Patients with relapsed or refractory plasma cell leukemia who have received at least two previous regimens
5. Patients at least 2 weeks from the last anti-myeloma therapy at the time of starting lymphodepleting chemotherapy. Patients may continue tyrosine kinase inhibitors or other targeted therapies until at least three days prior to administration of lymphodepleting chemotherapy. Small molecule targeted therapies will not include targeted immune therapies, such as daratumumab, isatuximab or elotuzumab.
6. Prior autologous/allogeneic transplants are allowed.
7. Prior cell therapy is allowed against targets other than NY-ESO-1.
8. Patients must have recovered from systemic toxicity of prior anti-myeloma therapy at the start of lymphodepletion.
9. No active or uncontrolled infection at the start of lymphodepletion and/or cell infusion.
10. No therapeutic systemic corticosteroids (\>/= 20 mg prednisone or equivalent) within 72 hours of lymphodepleting therapy.
11. Patients with concurrent autoimmune diseases with neurologic involvement, such as multiple sclerosis will be excluded.
12. Localized radiotherapy to one or more disease sites is allowed prior the infusion provided that there are additional disease sites that are not irradiated
13. Karnofsky Performance Scale \> 50%.
14. Adequate organ function:

1. Renal: Serum creatinine \/= 45 ml/min/1.73 m2.
2. Hepatic: ALT/AST \ 3. Cardiac: Cardiac ejection fraction \>/= 50%, no clinically significant pericardial effusion as determined by an ECHO or MUGA, and no uncontrolled arrhythmias or symptomatic cardiac disease.
4. Pulmonary: No clinically significant pleural effusion (per PI discretion), baseline oxygen saturation \> 92% on room air.
15. Able to provide written informed consent.
16. 18-80 years of age.
17. Weight ≥40 kg
18. All participants who are able to have children must practice effective birth control while on study and up to 3 months post completion of study therapy. Acceptable forms of birth control for female patients include: hormonal birth control, intrauterine device, diaphragm with spermicide, condom with spermicide, or abstinence, for the length of the study. If the participant is a female and becomes pregnant or suspects pregnancy, she must immediately notify her doctor. If the participant becomes pregnant during this study, she will be taken off this study. Men who are able to have children must use effective birth control while on the study. If the male participant fathers a child or suspects that he has fathered a child while on the study, he must immediately notify his doctor.
19. Signed consent to long-term follow-up protocol PA17-0483 to fulfill the institutional responsibilities to various regulatory agencies.
20. Participants must not have received any live vaccines within 30 days prior to enrollment.
21. No active infection requiring systemic antibiotics
22. Adequate bone marrow function without the need for transfusion in the last 7 days as described below, unless the pancytopenia is due to marrow replacement by myeloma:

* Absolute neutrophil count (ANC) ≥1000 /µL
* Hemoglobin ≥8 g/dL
* Platelet count ≥50,000 /µL
23. No bridging anti-myeloma therapy within 14 days of lymphodepleting therapy

Criteria for Cell Infusion-

Patients who meet one of the following criteria on the day of infusion will have their administration delayed for 24 hours. If these problems persist beyond 24 hours, patients will not receive their cell infusion.

1. cardiac arrhythmias not controlled with medical management
2. hypotension requiring vasopressor support
3. suspected or active uncontrolled infection

Exclusion Criteria:

1. None