Study of Combination Therapy With INCMGA00012 (Anti-PD-1), INCAGN02385 (Anti-LAG-3), and INCAGN02390 (Anti-TIM-3) in Participants With Select Advanced Malignancies

Inclusion Criteria: * Phase 1 Parts 1-4): Participants with locally advanced or metastatic solid tumors (locally advanced disease must not be amenable to resection with curative intent) that have failed available therapies, including anti-PD-(L)1 therapy if applicable, that are known to confer clinical benefit, or who are intolerant to, or ineligible for standard treatment. Prior anti-PD-(L)1 therapy should not have been discontinued because of intolerance. * Phase 2, Cohort A: 1. Participant with histologically confirmed unresectable/metastatic melanoma, whose disease failed prior anti-PD-(L)1 therapy (alone or as part of a combination) and meeting one of the following criteria: * Participant who failed prior adjuvant anti-PD-(L)1 therapy for resectable melanoma must have received prior anti-PD-(L)1 for ≥ 6 weeks and experienced disease progression while still on active adjuvant therapy containing anti-PD-(L)1, or participant who had early relapse occurring \< 24 weeks after end of adjuvant anti-PD-(L)1 therapy. Progressive disease must be ascertained by confirmatory biopsy collected at baseline. * Participant whose unresectable/metastatic disease progressed while on or within \< 24 weeks of completion of anti-PD-(L)1 for inresectable/metastatic melanoma. Progressive disease must have been confirmed by imaging ≥ 4 weeks after evidence of initial disease progression. 2. Participant must have received no more than 2 prior lines of therapy for melanoma and at least one prior regimen must have contained anti-PD-(L)1 therapy (alone or as part of a combination) either in the adjuvant and/or advanced/metastatic setting. 3. Participants must have had known BRAF V600 mutation status per local institutional testing standards. 4. Participants must have fresh biopsy available after completing prior PD-(L)1 therapy or be willing and able to safely undergo pretreatment tumor biopsies (core or excisional). Determination of whether participants can safely undergo biopsy should be made by the treating physician in consultation with the individual performing the biopsy. 5. Participant must have at least 1 measurable tumor lesion per RECIST v1.1. * Phase 2, Cohort B: 1. Participant with previously untreated, histologically confirmed Stage III (unresectable) or IV melanoma per the American Joint Committee on Cancer v8 staging system. 2. Participants must not have had prior systemic anticancer therapy for unresectable or metastatic melanoma. 3. Participants must have had known BRAF V600 mutation status per local institutional testing standards. 4. Participants must have fresh biopsy available or be willing and able to safely undergo pretreatment tumor biopsies (core or excisional). Determination of whether participants can safely undergo biopsy should be made by the treating physician in consultation with the individual performing the biopsy. * Phase 2 (Cohorts A and B): Participant must have at least 1 measurable tumor lesion per RECIST v1.1. * ECOG performance status 0 or 1. * Willingness to avoid pregnancy or fathering children Exclusion Criteria: * Laboratory and medical history parameters outside the protocol-defined range. * Known hypersensitivity or severe reaction to any component of the study drugs or formulation components ) within 14 days before study Day 1. * Participant who had prior treatment with a LAG-3 or TIM-3 targeted agent. Phase 1: (Parts 1-4): * Receipt of anticancer medications or investigational drugs within the following intervals before the first administration of study treatment: 1. ≤28 days or 5 half-lives (whichever is longer) before the first dose for all other investigational agents or devices. For investigational agents with long half-lives (eg, \> 5 days), enrollment before the fifth half-life requires medical monitor approval. 2. Administration of colony-stimulating factors (including granulocyte colony-stimulating factor, granulocyte macrophage colony-stimulating factor, or recombinant erythropoietin) within 14 days before study Day 1. * Phase 2: * Cohort A: Participant who has discontinued anti-PD-(L)1 therapy due to toxicity or other reasons unrelated to toxicity, then subsequently experienced disease progression. * Cohort A: Participant who had experienced objective response (PR/CR) and had stopped anti-PD-(L)1 therapy due to maximal benefit. * Cohort A: Participant with multiple metastases that achieved mixed tumor response to prior anti-PD-(L)1 therapy (such as isolated progressive lesion in a context of PR/CR or SD for other lesions) or achieved overall disease progression based only on a single new lesion. * Cohort B: Participant who has or has had uveal melanoma. * Receipt of anticancer therapy (immunotherapy, chemotherapy, targeted therapy or hormonal therapy) within 21 days of the first administration of study treatment, with the exception of localized radiotherapy. * Palliative radiation therapy administered within 1 week of first dose of study treatment or radiation therapy in the thoracic region that is \> 30 Gy within 6 months of the first dose of study treatment. * If participant received major surgery, then they must have recovered adequately from toxicities and/or complications from the intervention before starting study treatment. * Treatment-related toxicity related to prior therapy that has not recovered to ≤ Grade 1 (with the exception of alopecia and anemia not requiring transfusional support), unless approved by the medical monitor. * History of immune-related toxicity during prior checkpoint inhibitor therapy for which permanent discontinuation of therapy is recommended (per product label or consensus guidelines), OR any immune-related toxicity requiring intensive or prolonged immunosuppression to manage (with the exception of endocrinopathy that is well controlled on stable dose of replacement hormones such as hypothyroidism or adrenal insufficiency, or Grade 3 rashes that resolved with topical therapy or asymptomatic lipase elevations that do not require treatment interruption or uveitis that resolved with steroid drops). * Has an active autoimmune disease requiring systemic immunosuppression with corticosteroids (\> 10 mg/day of prednisone or equivalent) or immunosuppressive drugs within 14 days before the first dose of study treatment. * Receiving chronic systemic corticosteroids (\> 10 mg/day of prednisone or equivalent). * Active infections requiring systemic antibiotics, or antifungal or antiviral treatment within 7 days before first dose of study treatment. * History of organ transplant, including allogeneic stem cell transplantation. * Evidence of interstitial lung disease or active, noninfectious pneumonitis. * Known active HBV or HCV infection or risk of reactivation of HBV or HCV. * Participants who are known to be HIV-positive . * Known active brain or CNS metastases including carcinomatous meningitis. * Known additional malignancy that is progressing or requires active treatment, or history of other malignancy within 2 years of study entry with the exception of cured basal cell or squamous cell carcinoma of the skin, superficial bladder cancer, carcinoma in situ of the cervix, or other noninvasive or indolent malignancy after treatment with curative intent. * Participants with impaired cardiac function or clinically significant cardiac disease * History or presence of an abnormal ECG that, in the investigator's opinion, is clinically meaningful. * Women who are pregnant or breastfeeding. * Receipt of a live vaccine within 30 days of planned start of study treatment.