A Clinical Study of the Safety and Activity of the Investigational Cell Therapy NEO-PTC-01 in Patients With Advanced Melanoma

Inclusion Criteria: * Adult (age 18 to 75) men and women willing and able to give written informed consent. * Histologically confirmed unresectable or metastatic melanoma. * Part 1: * Have previously received a PD-1/PD-L1 inhibitor (either as single agent or in combination) and a cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) inhibitor-containing regimen (single agent or combination) prior to NEO-PTC-01, with disease progression following these therapies or otherwise lack of clinical benefit as determined by the study investigator. * Part 2: * Have received/are currently receiving a PD-1/PD-L1 inhibitor (as a single agent or in combination with CTLA-4) for at least 3 months. * Have documented SD by RECIST v1.1 or clinically asymptomatic progressive disease on the most recent imaging assessment, which must have occurred within 3 months of enrollment. * In the opinion of the investigator, are medically eligible and able to continue with PD-1/PD-L1 inhibitor therapy. * In the opinion of the investigator, would benefit from the addition of a T-cell based therapy. * For known serine-threonine kinase (BRAF) mutant patients: Patients must have also received targeted therapy (B-Raf inhibitor or B-Raf/mitogen-activated protein kinase enzyme \[MEK\] combination therapy) prior to NEO-PTC-01, unless deemed not appropriate to receive these treatments by the investigator. * Have at least one site of measurable disease by RECIST v1.1. * At least one site of disease must be accessible to biopsy for tumor tissue for sequence and immunological analysis. The biopsy site may be the same as the measurable site so long as it remains measurable. Surgical resection of the measurable site may not be performed if that site is the only measurable lesion. An archival biopsy may be used in place if the biopsy was taken within 6 months of informed consent. * Have Eastern Cooperative Oncology Group Performance Status of 0 or 1. * Recovered from all toxicities associated with prior treatment to acceptable baseline status (for laboratory toxicities see below limits for inclusion) or a National Cancer Institute Common Terminology Criteria for Adverse Events version 5.0, Grade of 0 or 1, except for toxicities not considered by the treating physician to be a safety risk (e.g., alopecia). * Screening laboratory values must meet the following criteria and should be obtained prior to any Production phase assessments: 1. White blood cell count ≥ 3 × 10\^3/μL. 2. Absolute neutrophil count ≥ 1.5 × 10\^3/μL. 3. Platelet count ≥ 100 × 10\^3/μL. 4. Hemoglobin \> 9 g/dL or 6 mmol/L. 5. Serum creatinine ≤ 1.5 × upper limit of normal (ULN) or creatinine clearance ≥ 50 mL/min by Cockcroft-Gault. 6. Aspartate aminotransferase and alanine aminotransferase ≤ 3 × ULN. 7. Total bilirubin ≤ 1.5 × ULN (except in patients with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dL). 8. International Normalized Ratio, Prothrombin Time (PT), or Activated Partial Thromboplastin Time (aPTT) ≤ 1.5 × ULN unless the patient is receiving anticoagulant therapy, as long as PT or aPTT is within therapeutic range of intended use of anticoagulants. Exclusion Criteria: * Age greater than 75 years or less than 18 years. * Prior cell therapy (including tumor-infiltrating lymphocyte, chimeric antigen receptor T cell, and T-cell receptor-based products) within 12 months prior to signing of informed consent form. * Have an active or history of autoimmune disease (known or suspected). Exceptions are permitted for vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition requiring only hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger. * Have known active central nervous system metastases and/or carcinomatous meningitis. Patients with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging \[using the identical imaging modality for each assessment, either MRI or CT scan\] for at least 4 weeks prior to enrollment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to enrollment. This exception does not include carcinomatous meningitis, which is excluded regardless of clinical and/or radiographic stability. * Active systemic infections requiring intravenous antimicrobial therapy, coagulation disorders or other active major medical illnesses of the cardiovascular, respiratory or immune system, as evidenced by a positive stress thallium or comparable test, myocardial infarction, clinically significant cardiac arrhythmias such as uncontrolled atrial fibrillation, ventricular tachycardia, or second- or third-degree heart block, and obstructive or restrictive pulmonary disease. * Active major medical illnesses of the immune system including conditions requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days prior to NEO-PTC-01 infusion. Inhaled or topical steroids and adrenal replacement doses (≤ 10 mg daily prednisone equivalents) are permitted in the absence of active autoimmune disease. * Known human immunodeficiency virus infection, active chronic hepatitis B or C, and/or life-threatening illnesses unrelated to cancer that could, in the investigator's opinion, interfere with participation in this study. * Have any underlying medical condition, psychiatric condition, or social situation that, in the investigator's opinion, would interfere with participation in the study. * Have a planned major surgery that is expected to interfere with study participation or confound the ability to analyze study data. * Are pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 150 days after the end of the trial visit. Nursing women are excluded from this study because there is an unknown but potential risk of AEs in nursing infants secondary to treatment of the mother with treatments to be administered in this study. * Have a history of another invasive malignancy aside from melanoma, except for the following circumstances: 1. Patient has been disease-free for at least 2 years and is deemed by the investigator to be at low risk for recurrence of that malignancy. 2. Patient was not treated with systemic chemotherapy for carcinoma in situ of the breast, oral cavity, or cervix, basal cell, or squamous cell carcinoma of the skin.