Antigen-specific T Cell Therapy for Patients With Relapsed Refractory Multiple Myeloma

Inclusion Criteria: 1. Ability to provide informed consent and documentation of informed consent prior to initiation of any study-related tests or procedures that are not part of standard-of-care for the patient's disease. Patients must also be willing and able to comply with study procedures, including the acquisition of specified research specimens 2. Age ≥ 18 years old \& life expectancy \> 3 months 3. Expression of HLA-A\*0201 as determined by high resolution sequence-based typing method 4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 with exception of ECOG \> 1 if related to recent bone fracture 5. Patients must have confirmed diagnosis of MM 6. Have identified relapsed/refractory disease which includes: 1. Previous therapy consisting of at least three (3) standard regimens, including a proteasome inhibitor, IMiD, or anti-CD38 targeting therapy. Note: Induction therapy, autologous stem cell transplantation (ASCT) \& maintenance therapy if given sequentially without intervening progressive disease (PD) are considered one 'regimen' 2. Refractory MM may be defined as disease that is refractory to treatment while on therapy or that shows progression within 60 days of the last therapy. 7. Have measurable disease as defined by: 1. Serum M protein ≥ 0.5 g/dL 2. Urine M protein ≥ 200 mg/24hr 3. Serum free light chains (FLC) ≥ 10 mg/dL with abnormal FLC ratio Note: Patients with IgA MM in whom serum protein electrophoresis (sPEP) is deemed unreliable, due to co-migration of normal serum proteins with the paraprotein in the β region, may be considered eligible as long as total serum IgA level is \> normal range. 8. Acceptable laboratory parameters as follows: 1. AST/ALT ≤ 2.5 × ULN 2. Total bilirubin ≤ 1.5 × ULN, except patients with Gilbert's syndrome, who may enroll if the conjugated bilirubin is within normal limits 3. Serum creatinine ≤ 2.5 mg/dL or estimated creatinine clearance (CL) ≥ 30 mL/min \& not dialysis-dependent 4. ALC \> 1000 cells/µL 9. Recovery to Grade 1 or baseline of non-hematologic toxicities from prior treatments, excluding alopecia \& Grade 2 peripheral neuropathy 10. Female patients of childbearing potential must test negative for pregnancy at enrollment and during the study. Sexually active women of child-bearing potential, unless surgically sterile, must be willing to use a highly effective method of birth control defined as those which result in a low failure rate (i.e., less than 1% per year) such as implants, injectables, combined oral contraceptives, intra-uterine devices (IUDs) or vasectomized partner 11. Male patients with partners of childbearing potential must be either vasectomized or agree to use a condom in addition to having their partners use another method of contraception resulting in a highly effective method of birth control defined as those which result in a low failure rate (i.e., less than 1% per year) such as implants, injectables, combined oral contraceptives, or IUDs. Patients should not have sexual intercourse with females who are either pregnant or lactating without double-barrier contraception • Is not pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the prescreening or screening visit through one year from administration of NEXI-002 T cells Exclusion Criteria: 1. Have active cerebral or meningeal disease related to the underlying malignancy 2. Have hemolytic anemia, plasma cell leukemia, Waldenstrom's macroglobulinemia, POEMS syndrome, amyloidosis, plasmacytoma, significant autoimmune or other malignant disease 3. History of allogeneic hematopoietic stem cell transplantation 4. Have active or uncontrolled infections with positive cultures and/or requiring treatment with IV anti-infective agents 5. Echocardiogram or MUGA with left ventricular ejection fraction \< 45% 6. History of clinically significant cardiovascular disease including but not limited to: 1. Myocardial infarction or unstable angina within the 6 months prior to the initiation of study 2. Stroke or transient ischemic attack within 6 months prior to initiation of study 3. Clinically significant cardiac arrhythmia 4. Uncontrolled hypertension: systolic blood pressure (SBP) \> 180 mmHg, diastolic blood pressure (DBP) \> 100 mmHg 5. Congestive heart failure (New York Heart Association \[NYHA\] class III-IV) 6. Pericarditis or clinically significant pericardial effusion 7. Myocarditis 7. Clinically significant pulmonary compromise, including a requirement for supplemental oxygen use to maintain adequate oxygenation 8. Eligible patients will not be on any steroids ≥10 mg per day prednisone or equivalent or other immunosuppressants such as tacrolimus, cyclosporine, etc. a. Intermittent topical, inhaled or intranasal corticosteroids are allowed 9. History of symptomatic deep vein thrombosis (DVT) or pulmonary embolism (PE) requiring systemic anticoagulation within 6 months before enrollment 10. History of autoimmune disease (e.g., Crohn's, rheumatoid arthritis, systemic lupus erythematosus, etc.) resulting in end organ injury or requiring systemic immunosuppression / systemic disease modifying agents within the last 2 year prior to enrollment. Subjects with a history of autoimmune-related hypothyroidism on a stable dose of thyroid replacement hormone and subjects with controlled Type 1 diabetes mellitus on a stable insulin regimen may be eligible for the study 11. Human immunodeficiency virus (HIV) seropositive; HIV testing within 2 years of enrollment 12. Seropositive for and with evidence of active viral infection with hepatitis B virus (HBV). Patients who are hepatitis B surface antigen (HBsAg) negative and HBV viral DNA negative are eligible 1. Patients who had HBV but have received an antiviral treatment and show non-detectable viral DNA for 6 months are eligible 2. Patients who are seropositive because of HBV vaccine are eligible 13. Seropositive for and with active viral infection with hepatitis C virus (HCV) a. Patients who had HCV but have received an antiviral treatment and show no detectable HCV viral DNA for 6 months are eligible 14. Second primary invasive malignancy that has not been in remission for more than 2 years. Exceptions that do not require a 2-year remission include: non-melanoma skin cancer; carcinoma in situ (cervix, bladder, breast, etc.) or squamous intraepithelial lesion on Pap smear; localized prostate cancer (Gleason score \< 6); or resected melanoma in situ 15. History of trauma or major surgery within 4 weeks prior to the initiation of study 16. Any serious underlying medical or psychiatric condition that would impair the ability of the patient to receive or tolerate the planned treatment and follow up 17. Known hypersensitivity to any component of NEXI-002 T cells, cyclophosphamide, fludarabine or tocilizumab 18. Vaccination with any live virus vaccine within 6 weeks prior to the initiation of study treatment. Inactivated annual influenza vaccination is allowed 19. Dementia or altered mental status that would preclude understanding and rendering of informed consent 20. History of seizures, aphasia, psychosis or other chronic clinically significant neurologic disorders a. Patients with remote history of seizures that are well controlled on anti-seizure medications and without any seizure episode for 6 months are eligible 21. Any issue that in the opinion of the investigator, would contraindicate the patient's participation in the study or confound the results of the study