• Must have a confirmed diagnosis of malignancy of their receptive histologies: unresectable or metastatic melanoma Stage IIIC to IV (Cohorts 1A,1B and 1C), advanced, recurrent or metastatic HNSCC (Cohort 2A), or Stage III or Stage IV non-small cell lung cancer (Cohorts 3A, 3B, and 3C). Stage IV NSCLC with no actionable mutations (EGFR, ALK, ROS1) with effective targeted therapy (Cohorts 3D and 3E).

• Cohorts 1A, 1D, 2A, 3A, 3D and 3E: If previously treated, patients must have progressed on or after most recent therapy and must not have received ICIs as part of one of the counted lines of prior therapy. Patients must have radiologically documented disease progression while receiving or after the completion of the most recent prior treatment. Patients may have received up to 3 prior systemic anticancer therapies (except for Cohort 3A, where patients whose tumors harbor actionable mutations may have received up to 4 prior systemic therapies). Patients in Cohort 1D may have had no prior therapy for advanced disease. Patients in Cohorts 3D and 3E may have had no prior systemic therapy for Stage IV disease.

• Cohorts 1B, 1C, 3B, and 3C: Unresectable or metastatic melanoma patients in Cohorts 1B or 1C must have previously received systemic therapy with a PD-1 blocking antibody. NSCLC patients in Cohort 3B must have previously received systemic therapy with any ICI (except for those patients with known oncogene driver mutations that are sensitive to targeted therapies) as part of 1 - 3 prior lines of therapy. NSCLC patients in Cohort 3C must have previously received 1 line of ICI monotherapy. No other systemic therapy for metastatic disease is allowed. Prior chemoradiation and/or chemotherapy in the adjuvant and/or neoadjuvant settings are allowed.

• Must have at least 1 resectable lesion

• Must have remaining measurable disease as defined by RECIST 1.1 following tumor resection

• Must be ≥ 18 years at the time of consent for Cohorts 1A, 1C, 1D, 2A, 3A, 3B, 3C, 3D and 3E. Patients must be ≥ 12 years at the time of consent for Cohort 1B. Enrollment of patients \> 70 years of age may be allowed after consultation with the Medical Monitor.

• Must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1, and an estimated life expectancy of ≥ 6 months.

• Patients of childbearing potential or those with partners of childbearing potential must be willing to practice an approved method of birth control during treatment and for 12 months after their last dose of aldesleukin, 4 months after their last dose of pembrolizumab, 5 months after their last dose of ipilimumab or nivolumab, or nivolumab-relatlimab; 6 months after the last dose of carboplatin; 14 months after the last dose of cisplatin; and 6 months after the last dose of pemetrexed, paclitaxel, or nab-paclitaxel, whichever occurs later.