A Study of Botensilimab (AGEN1181) for the Treatment of Advanced Melanoma

Inclusion Criteria: To participate in the study, participants must meet all the following inclusion criteria: Cohort A only: 1. Prior treatment with anti-PD-(L)1 therapy (for example, pembrolizumab or nivolumab) for at least 6 weeks and radiologic progression confirmed by 2 scans at least 4 weeks apart, or if symptomatic due to progressive malignancy, then 1 scan showing progression is sufficient. 2. Progression must be either on treatment with anti-PD-(L)1 regimen or ≤ 12 weeks from last anti-PD-(L)1 dose in metastatic setting or ≤ 24 weeks from completion of therapy in adjuvant/ neoadjuvant setting. 3. For Part 2 only, no intervening anti-cancer therapy between the last course of anti-PD-(L)1 treatment and the first dose of study treatment except for local measures (for example, surgical excision, biopsy, focal radiation therapy), or BRAF ± MEK inhibition when applicable in BRAF mutant participants. Cohort B only: 1. Prior treatment with first-generation anti-CTLA-4 therapy (for example, ipilimumab or tremelimumab) and prior treatment with anti-PD-(L)1 for at least 6 weeks. 2. Progression on most recent anti-cancer therapy. 3. For Part 2 only, no more than 3 prior lines of therapy in the advanced setting for BRAF mutant and no more than 2 prior lines of therapy in the advanced setting in the BRAF wild type. Cohorts A and B: 1. Voluntarily agree to participate by giving signed, dated, and written informed consent prior to any study-specific procedures. 2. Histologically confirmed Stage III (unresectable) or Stage IV histologically confirmed cutaneous melanoma as per the American Joint Committee on Cancer 8th edition staging system. 3. Measurable disease on baseline imaging per RECIST 1.1 criteria. 4. BRAF V600 mutation status or consent to BRAF V600 mutation testing per local institutional standards during the screening period. 5. Life expectancy ≥ 3 months. 6. Eastern Cooperative Oncology Group performance status of 0 or 1. 7. Adequate organ function is defined as the following laboratory values within 14 days of Cycle 1 Day 1 (C1D1): 1. Neutrophils \> 1500/microliter (μL) (stable off any growth factor within 4 weeks of first study treatment administration). 2. Platelets \> 100 × 10\^3/μL (transfusion to achieve this level is not permitted within 2 weeks of first study treatment administration). 3. Hemoglobin \> 8.0 grams/deciliter (g/dL) (transfusion to achieve this level is not permitted within 2 weeks of first study treatment administration). 4. Creatinine clearance ≥ 45 milliliters/minute (measured or calculated using modification of diet in renal disease). 5. Aspartate aminotransferase/alanine aminotransferase \< 3.0 × upper limit of normal (ULN). 6. Total bilirubin \< 1.5 × ULN, or \< 3.0 × ULN for participants with Gilbert syndrome. 7. Albumin ≥ 3.0 g/dL. 8. International normalized ratio or prothrombin time ≤ 1.5 × ULN and activated partial thromboplastin time ≤ 1.5 × ULN (unless participant is receiving anticoagulant therapy). 8. Participant must provide a formalin-fixed paraffin-embedded tumor tissue sample from the most recent biopsy of a tumor lesion, obtained within 90 days from signing informed consent form. If recent tumor tissue is unavailable or inadequate, a fresh biopsy will be required, unless the Sponsor agrees that it is not safe/feasible. 9. Women of childbearing potential (WOCBP) must have a negative urine or serum pregnancy test at screening (within 72 hours of first dose of study medication) and prior to study drug administration. In part 1, WOCBP must agree to use highly effective contraceptive measures starting with the screening visit through 3 months after the last dose of study treatment. In Part 2, WOCBP must agree to use highly effective contraceptive measures starting with the screening visit through 5 months after the last dose of study treatment. Note: Abstinence is acceptable if this is the established and preferred contraception for the participant. 10. In Part 1, male participants with a female partner(s) of childbearing potential must agree to use highly effective contraceptive measures throughout the study, starting with the screening visit through 3 months after the last dose of study treatment is received. In Part 2, male participants with a female partner(s) of childbearing potential must agree to use highly effective contraceptive measures throughout the study starting with the screening visit through 5 months after the last dose of study treatment is received. Males with pregnant partners must agree to use a condom; no additional method of contraception is required for the pregnant partner. Exclusion Criteria: To participate in the study, participants must meet none of the following exclusion criteria: Cohort A: 1\. Received prior anti-CTLA-4 therapy. Cohort B: 1\. Received prior Fc-engineered or Fc-enhanced anti-CTLA-4 therapy (for example, BMS-96218, BMS-986288, HBM4003, XTX101, CTLA-4 targeting bispecific or other approaches such as ONC-392). Cohorts A and B: 1. Ocular, uveal, or mucosal melanoma. 2. Any persistent toxicities (Common Terminology Criteria for Adverse Events \[CTCAE\] Grade ≥ 2) from prior cancer therapy, excluding endocrinopathies stable on medication, stable neuropathy, and alopecia. 3. Any history of CTCAE Grade ≥ 3 immune-mediated toxicity (excluding endocrinopathies and non-necrotizing/bullous rash) from prior checkpoint inhibitor therapy that required treatment with systemic corticosteroids (\> 10 mg/day prednisone or equivalent) or other immunosuppressive medications for more than 4 weeks. 4. Refractory ascites require 2 or more therapeutic paracentesis in the last 4 weeks or ≥ 4 within the last 90 days prior to study entry. 5. Bowel obstruction within the past 3 months or an impending bowel obstruction. 6. Clinically significant (that is, active) cardiovascular disease: cerebral vascular accident/stroke or myocardial infarction within 6 months of enrollment, unstable angina, congestive heart failure (New York Heart Association class ≥ III), or serious uncontrolled cardiac arrhythmia requiring medication. 7. Active brain metastases or leptomeningeal metastases with the following exceptions: 1. Treated brain metastases require a) surgical resection, or b) stereotactic radiosurgery. These participants must be off steroids ≥ 10 days prior to randomization for the purpose of managing their brain metastases. Repeat brain imaging following surgical resection or stereotactic radiosurgery is not required if their last brain magnetic resonance imaging is within screening window. Whole-brain radiation is not allowed. 2. Untreated isolated brain metastases that are too small for treatment by surgical resection or stereotactic radiosurgery (for example, 1-2 millimeters) and/or of uncertain etiology are potentially eligible but need to be discussed with and approved by the study Medical Monitor. 8. Concurrent malignancy (present during screening) requiring treatment or history of prior malignancy active within 2 years prior to the first dose of study treatment (that is, participants with a history of prior malignancy are eligible if treatment was completed at least 2 years before the first dose of study treatment and the participant has no evidence of disease). Participants with history of prior early-stage basal/squamous cell skin cancer, low-risk prostate cancer eligible for active surveillance or noninvasive or in situ cancers who have undergone definitive treatment at any time are also eligible. 9. Incomplete resolution of clinically significant adverse events related to most recent therapy/intervention prior to enrollment. 10. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine or booster \< 7 days before C1D1. For vaccines requiring more than 1 dose, the full series should be completed prior to C1D1, when feasible. A booster shot is not required but if given, must be administered \> 7 days from C1D1 or \> 7 days from future cycle on study. 11. Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients. 12. Any evidence of current interstitial lung disease (ILD) or pneumonitis or a prior history of ILD or non-infectious pneumonitis requiring high-dose glucocorticoids. 13. History of allogeneic organ transplant, stem cell transplant or bone marrow transplant (autologous stem cell transplant \> 5 years prior to study enrollment with no evidence of disease are eligible unless lymphopenia Grade \> 1 is present). 14. Psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study. 15. Participants with a condition requiring systemic treatment with either corticosteroids (\> 10 milligrams \[mg\] daily prednisone equivalent) within 14 days or another immunosuppressive medication within 30 days of the first dose of study treatment. Inhaled or topical steroids, and adrenal replacement steroid doses \> 10 mg daily prednisone equivalent, are permitted in the absence of active autoimmune disease. 16. Active autoimmune disease or history of autoimmune disease that required systemic treatment within 2 years before starting study treatment (that is, with use of disease-modifying agents or immunosuppressive drugs). 17. History or current evidence of any condition, co-morbidity, therapy, any active infections, or laboratory abnormality that might confound the results of the study, interfere with the participants participation for the full duration of the study, or is not in the best interest of the participant to participate, in the opinion of the treating Investigator. 18. A WOCBP who is pregnant or breastfeeding or WOCBP who are not willing to employ effective birth control from screening to 90 days after the last dose of botensilimab (whichever is later). 19. Previous SARS-CoV-2 infection within 10 days for mild or asymptomatic infections or 20 days for severe/critical illness prior to C1D1. 20. Uncontrolled infection with human immunodeficiency virus (HIV). Participants on stable highly active antiretroviral therapy with undetectable viral load and normal cluster of differentiation 4 counts for at least 6 months prior to study entry are eligible. Serological testing for HIV at screening is not required. 21. Known to be positive for hepatitis B virus (HBV) surface antigen, or any other positive test for HBV indicating acute or chronic infection. Participants who are receiving or who have received anti-HBV therapy and have undetectable HBV DNA for at least 6 months prior to study entry are eligible. Serological testing for HBV at screening is not required. 22. Known active hepatitis C virus (HCV) as determined by positive serology and confirmed by polymerase chain reaction (PCR). Participants on or who have received antiretroviral therapy are eligible, provided they are virus-free by PCR for at least 6 months prior to study entry. Serological testing for HCV at screening is not required. 23. Dependence on total parenteral nutrition.