To learn if KSQ-001EX is safe to give to participants with advanced forms of solid tumors.

Phase I Primary Objectives • To evaluate the safety and tolerability of KSQ-001EX in adult participants with advanced solid tumors (melanoma, HNSCC, NSCLC)

Phase I Primary Endpoint

• Incidence of dose-limiting toxicities (DLTs)

Phase I Secondary Objectives

• Determine expansion dose
• Assess the safety and tolerability of KSQ-001EX in participants with advanced solid tumors (melanoma, HNSCC, NSCLC)
• Evaluate preliminary antitumor activity of KSQ-001EX in participants with advanced solid tumors
• Evaluate the feasibility of the manufacturing process.

Phase I Secondary Endpoints

• Incidence and severity of treatment-emergent adverse events (TEAEs) and change from Baseline in laboratory results
• Objective response rate (ORR), duration of response (DOR), time to response (TTR) as assessed by the Investigator, per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1
• Manufacturing success rate

Phase 2 Primary Objectives • To assess the anti-tumor activity of KSQ-001EX in patients with advanced malignant solid tumors

Phase 2 Primary Endpoint

• ORR per RECIST v1.1

Phase 2 Secondary Objectives

• Assess the safety and tolerability of KSQ-001EX in patients with advanced solid tumors (melanoma, HNSCC, NSCLC)
• Evaluate anti-tumor activity of KSQ-001EX in patients with advanced malignant solid tumors
• Evaluate overall survival (OS)
• Evaluate the feasibility of the manufacturing process

Phase 2 Secondary Endpoints

• Incidence and severity of TEAEs and change from Baseline in laboratory results
• Complete response rate (CRR), DOR, TTR, progression-free survival (PFS) per RECIST v1.1
• OS
• Manufacturing success rate

Phase 1/2 Exploratory Objectives

• Determine persistence of KSQ-001EX
• Assess changes in immune and pharmacodynamic markers following KSQ-001EX infusion
• Assess correlations of KSQ-001EX biomarkers and KSQ-001EX DP characteristics with safety, clinical activity, and KSQ-001EX persistence

Phase 1/2 Exploratory Endpoints

• KSQ-001EX levels in blood and tumor tissue
• Change from Baseline in soluble immune factors, lymphocytes and immune markers
• KSQ-001EX pharmacodynamic markers, KSQ-001EX DP release criteria, and KSQ-001EX persistence

Inclusion Criteria:

• Diagnosed with one of the following tumor types:

1. Unresectable, incurable and/or metastatic histologically and/or cytologically confirmed melanoma (Stage IIIC/IIID or Stage IV) that has progressed following at least 1 line of prior systemic therapy including treatment with anti-PD-1/PD-L1 inhibitor alone or in combination with anti-CTLA-4 inhibitor or anti-LAG-3 antibody. Note: Up to 5 mucosal melanoma patients can be treated in melanoma expansion cohort only.
2. Histologically and/or cytologically confirmed primary diagnosis of NSCLC which has progressed on standard therapy which includes treatment with 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 EGFR, ALK, ROS-1, BRAF, RET, MET and KRAS must have progressed on standard directed molecular therapy in addition to platinum-based chemotherapy.

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 3 lines of prior therapy

i. Participants must have received a platinum-containing chemotherapy regimen for the treatment of primary tumor in locally advanced, or metastatic setting.

ii. Participants must have received an anti-PD-1/PD-L1 as monotherapy or in combination with chemotherapy • Resectable lesion(s) for KSQ-001EX manufacturing (tumor ≥1.5cm2 or at least 5 core biopsies)

• At least 1 measurable lesion per RECIST v1.1 (Eisenhauer 2009) following tumor resection for KSQ-001EX 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

• Age: between 18 - 70 years old

• Life expectancy of ≥ 12 weeks

• Recovered to ≤ Grade 1 or Baseline toxicity (except alopecia, neuropathy, and endocrinopathies from prior immunotherapy) from prior therapy (per CTCAE)

• Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1

• 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

• Adequate renal function defined as calculated creatinine clearance (Cockcroft-Gault) ≥ 40 mL/min

• Adequate hepatic function defined as:

  1. Total bilirubin ≤ 2.0 × upper limit of normal (ULN) unless associated with Gilbert's syndrome
  2. Aspartate aminotransferase and alanine aminotransferase ≤ 3.0 × ULN (or ≤ 5 × ULN in patients with liver metastases)

• Washout period from prior anticancer therapy(ies) of a minimum duration (excluding bridging therapy per Concomitant Medication, Section 6.4) is required prior to the first study treatment (ie, start of LDC therapy) as detailed below:

  1. Targeted therapy: prior targeted therapy with a BRAK/MEK, EGFR, ALK, receptor tyrosine kinase, or other-directed agent (eg, erlotinib, afatinib, osimertinib, crizotinib, ceritinib), is allowed provided the washout is a minimum of 21 days or 5 half-lives, whichever is longer prior to start of therapy (LDC)
  2. Monoclonal antibodies within 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)

• Female participants who are women of childbearing potential (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-001EX infusion). Male participants must be willing to use effective barrier contraception (ie, condoms) during the study treatment period and for up 3 months after study treatment (KSQ-001EX infusion)

• Capable of understanding and complying with protocol requirements

• Signed and dated Institutional Review Board (IRB) approved informed consent form before any protocol-directed Screening procedures are performed

Exclusion Criteria:

• Prior organ allograft or prior cell therapy that included LDC or myeloablative chemotherapy regimen

• Known hypersensitivity to any component of KSQ-001EX or excipient including dimethyl sulfoxide, human serum albumin, LDC regimen (cyclophosphamide or fludarabine) or IL-2 (as applicable)

• Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease [eg, Grade ≥2 colitis or Crohn's disease], systemic lupus erythematosus, sarcoidosis syndrome, or Wegener syndrome [granulomatosis with polyangiitis], rheumatoid arthritis, etc.]). The following are exceptions to this criterion:

  1. Participants with vitiligo or alopecia
  2. Participants with hypothyroidism (eg, following Hashimoto syndrome) stable on hormone replacement and stable doses of steroids after immune-mediated hydrophysitis/adrenal insufficiency
  3. Any chronic skin condition that does not require systemic therapy
  4. Participants with celiac disease controlled by diet alone

• Hypersensitivity to antibiotics of the aminoglycoside group (eg, streptomycin, gentamicin) or penicillin

• Active, uncontrolled concurrent infection requiring IV antibiotics present at Screening

• Uveal and/or ocular melanoma

• Large cell neuroendocrine NSCLC (defined as pathology with > 10% neuroendocrine components)

• Symptomatic and/or untreated brain metastases (of any size or number) including active leptomeningeal or parenchymal metastases. Note: Participants with definitively treated brain metastases may be considered for enrollment if stable (defined as stable for 1-month post-central nervous system directed therapy) and does not require ongoing steroid treatment

• Women who are pregnant or nursing

• Seropositive for human immunodeficiency virus (HIV) 1 or 2 or acquired immunodeficiency syndrome, or active infection with hepatitis B virus (HBV) or hepatitis C virus (HCV) Note: Participants with positive HCV antibody may be eligible if HCV ribonucleic acid [RNA] is undetectable on a quantitative HCV RNA assay, following discussion with the Sponsor

• Any form of primary immunodeficiency (eg, Severe Combined Immunodeficiency Disease)

• Any known clinically significant or concurrent acute liver disease, including viral hepatitis

• Previous solid organ or hematopoietic cell transplant

• Need for treatment with steroids at stable doses (> 10 mg/day prednisone or equivalent)

  1. Topical, ophthalmic, or inhaled steroid medications are allowed
  2. Systemic steroid (> 10 mg/day) use is not allowed for 14 days prior to enrollment
  3. Systemic steroids ≤ 10 mg/day are permitted if for supplemental endocrine only

• Live or unattenuated vaccine < 28 days prior to first dose of LDC regimen

• History of stroke, transient ischemic attack, unstable angina, or myocardial infarction, within 3 months prior to first dose of study treatment

• Symptomatic congestive heart failure according to New York Heart Association (NYHA) classification, Class III or IV (per NYHA Classification), unstable angina pectoris, clinically significant cardia arrhythmia, or left ventricular ejection fraction < 45%

• Prolongation of QT/QTc interval (QTc interval > 480 msec) using the Frederica method of QTc analysis

• Unable to walk a distance of 80% predicted for age and sex or develop hypoxia (SPO2 < 90%) during a 6-minute walk test (this test can be performed in place of pulmonary function test [PFT] for those unable to perform a reliable PFT due to complex upper airway anatomy)

• > 80% stenosis based on carotid doppler ultrasound for patients with NSCLC and HNSCC with > 35 pack year smoking history

• Obstructive or restrictive pulmonary disease

  • Post-bronchodilator values: forced expiratory volume (FEV1)/forced vital capacity > 70% or FEV1 > 50% of predicted normal are required for study entry

• Suspected active pneumonitis or interstitial lung disease (confirmed by radiography or computed tomography [CT])

• Treatment on another study with other investigational therapeutic interventional study within 28 days to start of LDC regimen

• Known additional malignancy that is active and/or progressive requiring treatment; exceptions including basal cell or squamous cell skin cancer, or other cancer for which the participant has been disease-free for at least 2 years

• Psychiatric illness that would limit compliance with study requirements, as determined by the Investigator

• Other severe, acute, or chronic medical condition or laboratory abnormality that may increase the risk associated with study participation or study drug administration, or that may interfere with the interpretation of the study results, and in the judgement of the Investigator, would the participant inappropriate for the study.