Inclusion Criteria:

        Among other criteria, patients must meet all of the following conditions to be eligible for
        the study:

          -  Unresectable, histologically-confirmed advanced (Stage III or Stage IV) melanoma

          -  Disease progression during or after the last anticancer therapy received. For Cohort
             3, progression must have occurred during the PD-1 targeted CPI (checkpoint inhibitor)
             treatment and the investigator has deemed it appropriate to continue treatment with
             the PD-1 targeted CPI beyond confirmed disease progression

          -  No more than one prior chemotherapy-containing regimen for advanced disease.

          -  Prior treatments received must include at least one CPI inhibitor (e.g., anti-CTLA-4,
             PD-1-, PD-L1-targeted immunotherapy) and for patients with a BRAF mutation at least
             one BRAF- or MEK-targeted therapy, unless patients are not candidates for, or refused,
             these therapies. For cohort 3, prior treatment received must include a PD-1 targeted
             CPI administered during the most recent disease progression and for patients with BRAF
             mutation at least one BRAF- or MEK-targeted therapy when appropriate

          -  The study site will submit paraffin-embedded tumor tissue obtained from the patient
             for gpNMB analysis. Patients may require a biopsy if recent tumor tissue is not
             available. Patients in cohort 2 and 3 must submit a recently obtained biopsy of the
             skin fold for gpNMB analysis. Patients in Cohort 4 will submit a tumor tissue sample
             while on study.

          -  Eastern Cooperative Oncology Group (ECOG) Performance Status 0 to 1

          -  Adequate bone marrow, liver and renal function.

        Exclusion Criteria:

        Among other criteria, patients who meet any of the following conditions are NOT eligible
        for the study:

          -  Previously received glembatumumab vedotin (CR011-vcMMAE, CDX-011) or other
             MMAE-containing agents

          -  Treatment with the following therapies before the planned start of study treatment:

               1. BRAF or MEK inhibitors within 2 weeks

               2. Monoclonal based therapies within 4 weeks except for the PD-1 targeted checkpoint
                  inhibitor in cohort 3

               3. Immunotherapy (tumor vaccine, cytokine, or growth factor given to control the
                  cancer) within 2 weeks

               4. Chemotherapy within 21 days or at least 5 half-lives (whichever is longer)

               5. Investigational therapy within 2 weeks (or at least 5 half-lives, whichever is
                  longer)

          -  Patients with ocular melanoma

          -  Neuropathy that is moderate (Grade 2) or worse.

          -  Cancer that has spread to the brain or spine will be discussed with the study sponsor
             and may exclude patients from the trial.

          -  History of another cancer except:

               1. Patients with adequately treated and cured non-melanoma skin cancer or in situ
                  cancer

               2. Patients with any other cancer from which the patient has been disease-free for ≥
                  3 years

          -  Significant cardiovascular disease

          -  Previously received varlilumab or any other anti-CD27 mAb (Cohort 2 only)

          -  Active systemic infection requiring treatment

          -  Treatment with immunosuppressive medications within 4 weeks or corticosteroids within
             two weeks

          -  Patients with interstitial lung disease (Cohort 3 only)

          -  Patients with active diverticulitis (Cohort 3 only)

          -  Any non-study vaccination within 4 weeks, or influenza vaccine within 2 weeks, prior
             to CDX-301 dosing (Cohort 4 only)