A Phase 1/2 Study of KSQ-004EX, Autologous Tumor Infiltrating Lymphocytes Engineered to Inactivate Genes Encoding SOCS1 and Regnase-1, in Patients With Select Advanced Solid Tumors

Inclusion Criteria: 1. Diagnosed with one of the following tumor types: 1. Unresectable, incurable and/or metastatic histologically and/or cytologically confirmed cutaneous, acral, or unknown primary melanoma (Stage IIIC or Stage IV) that has progressed following at least 1 and no more than 3 lines of prior therapy in the advanced/metastatic setting, one of which includes treatment with anti-PD-1/PD-L1 inhibitor alone or in combination with anti-cytotoxic T lymphocyte associated protein 4 (anti-CTLA-4) inhibitor or in combination with anti-LAG-3 antibody. Note: Up to 5 mucosal patients can be treated in the melanoma expansion cohort only. 2. Histologically and/or cytologically confirmed primary diagnosis of NSCLC which has progressed on at least 1 line and no more than 4 lines of prior therapy in the advanced/metastatic setting, including platinum-based chemotherapy and checkpoint inhibitor therapy (either given in combination or sequentially). i. Participants with tumors that have known actionable molecular alteration such as epidermal growth factor receptor (EGFR), anaplastic lymphoma kinase (ALK), ROS-1, B-Raf proto-oncogene (BRAF), rearranged during transfection (RET), MET and Kirsten Rat Sarcoma Virus (KRAS) must have progressed on standard directed molecular therapy in addition to platinum-based chemotherapy. Note, the following do not count towards a line of prior therapy: * Any therapy/regimen discontinued due to intolerance/tolerability issues * Retreatment with the same class or previous class of treatment alone or in combination c. Locally advanced recurrent and/or metastatic histologically and/or cytologically confirmed HNSCC that has been previously treated with at least 1 and no more than 4 lines of prior therapy in the advanced/metastatic setting. i. Participants must have received a platinum-containing chemotherapy regimen for the treatment of primary tumor in locally advanced, or metastatic setting d. Advanced, metastatic histologically and/or cytologically confirmed colorectal adenocarcinoma that has progressed following at least 1 and no more than 3 lines of prior therapy. Participants with dMMR/MSI-H or KRASG12C BRAF V600E mutation must have progressed on standard directed therapy. e. Locally advanced, recurrent, or metastatic histologically and/or cytologically confirmed pancreatic ductal adenocarcinoma (PDAC) that has progressed following at least 1 and no more than 3 lines of prior therapy in the advanced/metastatic setting. f. Recurrent, metastatic, or persistent histologically and/or cytologically confirmed squamous cell carcinoma (SCC), adenosquamous carcinoma, or adenocarcinoma of the cervix that is not amenable to curative treatment with surgery and/or radiation therapy that has progressed following at least 1 and no more than 3 lines of prior therapy in the advanced/metastatic setting. 2. Resectable lesion for KSQ-004EX manufacturing (tumor ≥ 1.5 cm2 or at least 5 core needle biopsies) 3. At least one measurable lesion per RECIST v1.1 (Eisenhauer 2009) following tumor resection for KSQ-004EX manufacturing Note: Lesions in previously irradiated areas should not be selected as a target lesion unless radiation treatment was ≥ 3 months prior, and there has been demonstrated disease progression in the lesion 4. Age ≥ 18 years of age 5. Life expectancy of ≥ 12 weeks 6. Recovered to ≤ Grade 1 or Baseline toxicity (except alopecia, neuropathy, and endocrinopathies from prior immunotherapy) from prior therapy (per the National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\]) 7. Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 8. Adequate bone marrow function defined as: 1. Absolute neutrophil count (ANC) of ≥ 1 × 109/L 2. Platelet count of ≥ 100.0 × 109/L 3. Hemoglobin of ≥ 9.0 g/dL 9. Adequate renal function defined as calculated creatinine clearance (Cockcroft-Gault) ≥ 40 mL/min 10. Adequate hepatic function defined as: 1. Total bilirubin ≤ 2.0 × upper limit of normal (ULN) unless associated with Gilbert's syndrome 2. Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3.0 × ULN (or ≤ 5 × ULN in patients with liver metastases) 11. Washout period from prior anticancer therapy(ies) of a minimum duration (excluding bridging therapy per concomitant medication, see Section 6.11) is required prior to the first study treatment (i.e., start of LDC therapy) as detailed below: 1. Targeted therapy: prior targeted therapy with an EGFR, ALK, receptor tyrosine kinase, or other-directed agent (eg, erlotinib, afatinib, osimertinib, crizotinib, ceritinib), is allowed provided the washout is a minimum of 7 days or 5 half-lives, whichever is longer prior to start of therapy (LDC) 2. Monoclonal antibodies with a washout of at least 21 days or 5 half-lives or whichever is longer 3. Chemotherapy: adjuvant, neoadjuvant or definitive chemotherapy/chemoradiation is allowed provided the washout is a minimum of 21 days or 5 half-lives, whichever is shorter 4. Radiation therapy: prior external beam radiation is allowed provided a minimum of 14 days have elapsed between the last dose of radiation and first study treatment (LDC) 5. Surgery: previous surgical procedure(s) is permitted provided that wound healing has occurred and at least 14 days have elapsed (for major operative procedures) prior to the first study treatment (LDC) 12. Female participants who are women of childbearing potential (WOCP), (defined as physiologically and anatomically capable of becoming pregnant), confirmed of a negative pregnancy test and agreement to the use of a highly effective contraceptive method or at least 2 effective methods at the same time during study treatment period and for up to 3 months after study treatment (KSQ-004EX infusion). Male participants must be willing to use effective barrier contraception (ie, condoms) during the study treatment perio