Different Doses of BI-1607 in Combination With Pembrolizumab and Ipilimumab, in Participants With Unresectable or Metastatic Melanoma

Inclusion Criteria: 1. Is willing and able to provide written informed consent for the trial. 2. Is ≥ 18 years of age on the day of signing informed consent. 3. Has histologically confirmed advanced melanoma (unresectable or metastatic melanoma) with established disease progression. 4. Participants must have progressed on treatment with an anti-PD-1/L1 mAb. Subjects with uveal melanoma are not required to have received any prior anti-PD-1/L1 treatment. PD-1 treatment progression is defined by meeting all of the following criteria: 1. Has received at least 2 doses of an approved anti-PD-1/L1 mAb. 2. Has demonstrated disease progression after anti PD-1/L1 as defined by RECIST v1.1. The initial evidence of disease progression is to be confirmed by a second assessment no less than four weeks from the date of the first documented disease progression, in the absence of rapid clinical progression. 3. Progressive disease has been documented within 12 weeks from the last dose of anti-PD-1/L1 mAb. 5. Participants may have received previous treatment with BRAF inhibitors alone or in combination with mitogen extracellular kinase (MEK) inhibitors. 6. Has at least 1 measurable disease lesion as defined by RECIST v1.1 criteria. 7. Must be willing to provide tumour biopsies as specified in the schedule of assessments (SoA) unless otherwise discussed and agreed with the Sponsor in case a biopsy cannot be taken for a medical/safety reason. 8. Has a life expectancy of ≥ 12 weeks. 9. Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. 10. Has adequate organ function as confirmed by laboratory values 11. Participants who are hepatitis B surface antigen (HBsAg) positive are eligible if they have received hepatitis B virus (HBV) antiviral therapy for at least 4 weeks and have undetectable HBV viral load prior to enrolment. 12. Participants with history of hepatitis C virus (HCV) infection are eligible if HCV viral load is undetectable at Screening. Exclusion Criteria: 1. Has previously been treated with an anti-CTLA-4 mAb or anti-LAG3 mAb (anti-Lymphocyte Activation Gene 3). 2. Has received any prior immunotherapy and was discontinued from that treatment due to a Grade 3 or higher irAE (except endocrine disorders that can be treated with replacement therapy) or was discontinued from that treatment due to Grade 2 myocarditis or recurrent Grade 2 pneumonitis. 3. Has received the following: 1. Chemotherapy or small molecule products within 4 weeks of first dose of BI-1607. 2. Radiotherapy within 2 weeks of first dose of BI-1607, or has radiation-related toxicities, requiring corticosteroids. Participants who have previously had radiation pneumonitis are not allowed. 3. Immunotherapy or biological anti-cancer therapy or an investigational agent or an investigational device within 4 weeks prior to the first dose of BI-1607. 4. Has not recovered from all AEs due to previous therapies to ≤ Grade 1 or baseline. 5. Has had major surgery from which the participant has not yet recovered or is scheduled to have major surgery \< 28 days prior to the first dose of trial intervention. 6. Has received a live or live-attenuated vaccine within 30 days prior to the first dose of trial intervention. 7. Is participating or planning to participate in another interventional clinical trial or has participated in a trial of an investigational agent or has used an investigational device within 4 weeks prior to first dose of trial intervention. 8. Has history of allogeneic tissue/solid organ transplant. 9. Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior the first dose of trial intervention . 10. Has a known additional malignancy that is progressing or has required active treatment within the past 3 years. 11. Has known active CNS metastases and/or carcinomatous meningitis. 12. Has severe hypersensitivity to (≥ Grade 3) to pembrolizumab and/or any of its excipients. Has known or suspected hypersensitivity to BI-1607, ipilimumab or any of their excipients. Previous isolated infusion related reactions (IRRs) are not to be considered a reason for exclusion unless Grade 4 in severity. 13. Has an active autoimmune disease that has required systemic treatment in past 2 years. 14. Has a history of (noninfectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. 15. Is at high medical risk because of non-malignant systemic disease including severe active infections on treatment with antibiotics, antifungals, or antivirals. 16. Has a known history of human immunodeficiency virus (HIV) infection. No HIV testing is required unless mandated by local health authority. 17. Has cardiac or renal amyloid light-chain amyloidosis. 18. Is a female participant and has the possibility to become pregnant (or already pregnant or lactating/breastfeeding). However, those female participants who have a negative serum or urine pregnancy test before enrolment and agree to use a highly effective method of birth control for 4 weeks before entering the trial, during the trial, and for 12 months after last dose of BI-1607 OR 4 months after the last dose of pembrolizumab, whichever is later are considered eligible. 19. Is a male participant with partner(s) of childbearing potential (unless he agrees to use a barrier method of contraception with the female partner(s) who are using one highly effective method of contraception during the trial and for 12 months after completing treatment). 20. Has uncontrolled or significant cardiovascular disease 21. Has a history or there is current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the participant's participation for the full duration of the trial, or in the opinion of the treating Investigator is not in the best interest of the participant to participate. 22. Has a known psychiatric or substance abuse disorder that would interfere with the participant's ability to cooperate with the requirements of the trial.