Inclusion Criteria:

          -  Is willing and able to provide written informed consent for the trial.

          -  Is ≥18 years of age on day of signing informed consent.

          -  Has a histologically confirmed advanced solid tumor. Subjects must have received at
             least 2 doses of an approved anti-PD-1/L1 mAb, and have documented progression on or
             within 12 weeks from the last dose of anti-PD-1/L1 mAb.

          -  Is intolerant of, refuses, or is not eligible for standard antineoplastic therapy.

          -  Has at least 1 measurable disease lesion as defined by Response Evaluation Criteria in
             Solid Tumors

          -  Is able to safely undergo a baseline tumor tissue biopsy prior to first dose of
             BI-1206

          -  Has a life expectancy of ≥12 weeks.

          -  Has an ECOG performance status of 0-1.

          -  Has adequate organ function as confirmed by laboratory values listed in the main body
             of the protocol

        Expansion Cohort-Specific Inclusion Criteria:

        In addition to the general inclusion criteria above, subjects must also meet the criteria
        for the specific cohort.

          -  Cohort 1 (Non-small cell lung cancer):

               -  For subjects whose tumor has PD-L1 ≥ 50%: Required prior therapies will include
                  anti-PD-1 therapy as monotherapy. Prior standard of care chemotherapy will be
                  allowed but not required.

               -  For tumors with unknown PD-L1 or PD-L1 < 50% , required prior therapies will
                  include anti-PD 1/PD-L1 therapy and SOC chemotherapy either combined with anti
                  PD-1/PD-L1 therapy or given separately.

               -  For subjects with known anaplastic lymphoma kinase, ROS1 or epidermal growth
                  factor receptor sensitizing molecular rearrangements, one line of targeted
                  therapy will be required in addition to anti-PD-1/PD-L1 therapy.

          -  Cohort 2 (Metastatic Melanoma):

               -  Required prior therapies will include anti-PD-1 therapy either as monotherapy or
                  as part of a combination regimen.

               -  For subjects with a known BRAF V600-activating mutation combination targeted
                  therapy will be required in addition to anti-PD-1/PD-L1 therapy.

          -  Cohort 3 (Other Tumor Types):

               -  All subjects will require prior anti-PD-1/PD-L1 therapy

        Exclusion Criteria:

          -  Needs doses of prednisolone >10 mg daily (or equipotent doses of other
             corticosteroids)

          -  Has known active central nervous system (CNS) metastases and/or carcinomatous
             meningitis.

          -  Has known or suspected hypersensitivity to pembrolizumab or BI-1206 or any of their
             excipients.

          -  Has cardiac or renal amyloid light-chain (AL) amyloidosis.

          -  Has received the following:

               -  Chemotherapy or small molecule products within 4 weeks of first dose of BI 1206.

               -  Radiotherapy within 2 weeks of first dose of BI-1206. A 1-week washout is
                  permitted for palliative radiation (≤2 weeks of radiotherapy) for non-CNS
                  disease. Subjects who have previously had radiation pneumonitis are not allowed.

               -  Immunotherapy within 4 weeks prior to the first dose of BI-1206.

          -  Has not recovered from AEs to at least Grade 1 by Common Terminology Criteria for
             Adverse Events v4.0 due to prior anti-cancer therapies.

          -  Has had Grade ≥3 autoimmune manifestations of previous immune checkpoint inhibitor
             treatments .

          -  Has a history of (non-infectious) pneumonitis that required steroids or has current
             pneumonitis.

          -  Has an active, known or suspected autoimmune disease.

          -  Is a female subject and has the ability to become pregnant (or already pregnant or
             lactating/ breastfeeding). o Intravaginal

          -  Is a male subject with partner(s) of child-bearing potential• Has had major surgery
             from which the subject has not yet recovered.

          -  Is at high medical risk because of non-malignant systemic disease including severe
             active infections on treatment with antibiotics, antifungals or antivirals.

          -  Has presence of chronic graft versus host disease.

          -  Has had an allogenic tissue/solid organ transplant.

          -  Has known human immunodeficiency virus (HIV) and / or history of hepatitis B or C
             infections, or has a positive test for HIV antibody, hepatitis B antigen / hepatitis B
             virus DNA or hepatitis C antibody or RNA.

          -  Has a history of active tuberculosis (bacillus tuberculosis).

          -  Has received a live vaccine within 30 days before the first dose of study treatment.

          -  Has uncontrolled or significant cardiovascular disease

          -  Has a known psychiatric or substance abuse disorder that would interfere with the
             subject's ability to cooperate with the requirements of the study.

          -  Has a history or current evidence of any condition, therapy, or laboratory abnormality
             that might confound the results of the study, interfere with the subject's
             participation for the full duration of the study, or is not in the best interest of
             the subject to participate, in the opinion of the treating investigator.

          -  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 study drug. Subjects who
             have entered the follow-up phase of an investigational study may participate as long
             as it has been 4 weeks after the last dose of the previous investigational agent.
             Participation in an observational trial is acceptable.

          -  Has a known additional malignancy of another type

          -  Has a diagnosis of primary or acquired immunodeficiency disorder or taking any other
             form of immunosuppressive therapy within 7 days prior the first dose of study drug.