• Signed, written informed consent obtained prior to any study procedures.

• Age \> 18 years at the time of informed consent.

• Metastatic solid tumor with ≥ 10% of tumor cells positive for KK-LC-1 by IHC assay. Due to the low frequency of KK-LC-1 expression in most cancers, screening will focus on gastric, NSCLC, TNBC, and cervix cancers. The IHC test will be performed by the Rutgers Cancer Institute, Department of Biorepository Services.

• HLA-A\*01:01 allele by HLA haplotype test.

• Measurable disease per RECIST Criteria Version 1.1 at time of enrollment.

• Prior treatment with cancer type-specific standard of care systemic cancer therapy is required. Standard treatment options must be considered and declined. Documentation of rationale is required if a subject is deemed unsuitable for standard therapy.

• Subjects with \< 3 brain metastases that have been treated with surgery or stereotactic radiosurgery are eligible. Lesions that have been treated with stereotactic radiosurgery must be clinically stable for one month before protocol treatment. Patients with surgically resected brain metastases are eligible.

• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 at screening.

• Negative pregnancy test for women under 55 and all women who have had a menstrual period in the last 12 months. A pregnancy tests is not required for women who have had a bilateral oophorectomy or hysterectomy.

⁃ Women of child-bearing potential must agree to use adequate contraception (i.e., intrauterine device, hormonal barrier method of birth control; abstinence; tubal ligation or vasectomy) prior to study entry and for 12 months after treatment. Should a women become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately.

⁃ Participants must have organ and marrow function as defined below:

• Leukocytes \> 3,000/mcL

∙ Absolute neutrophil count \> 1,500/mcL

∙ Platelets \> 100,000/mcL

∙ Hemoglobin \> 9.0 g/dL

∙ Total bilirubin within normal institutional limits except in participants with Gilbert's Syndrome who must have a total bilirubin \< 3.0 mg/dL.

∙ Serum AST (SGOT)/ALT (SGPT) \< 2.5 x ULN

∙ Calculated creatinine clearance (CrCl) \>50 mL/min/1.73 m2for participants with creatinine levels above institutional normal (by the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation).

∙ INR or a PTT ≤1.5 X ULN unless the subject is receiving anticoagulant therapy. Subjects on anticoagulant therapy must have a PT or PTT within therapeutic range and no history of severe hemorrhage.

⁃ Serology:

∙ HIV antibody negative

‣ Hepatitis B antigen negative

‣ Hepatitis C antibody negative or HCV RNC negative (i.e., no current HCV infection)

⁃ More than four weeks must have elapsed since any prior systemic therapy at the time the patient receives the KK-LC-1 TCR T cells. Adverse events from prior therapy must have resolved to ≤ grade 1 according to CTCAE Version 5.0 or have demonstrated clinical stability and meet the eligibility criteria for the protocol.

⁃ Oxygen saturation ≥ 92% on room air.

⁃ Left ventricular ejection fraction ≥45% by echocardiogram or MUGA for patients 50 years of age or older.