Inclusion Criteria:

        • Participants enrolled into Part 1 must have tumor lesions where repeated IT injections
        are not feasible and in whom, based on the Investigator's judgement, SC injection is the
        only viable route of CMP-001 administration. Participants with lesions that are easily
        accessible for IT injections are not eligible to participate in Part 1. Participants
        enrolled into Part 2 must have at least one tumor lesion with a longest diameter of >/= 0.5
        cm amenable for IT injection of CMP-001.

        All participants enrolled into either Part 1 or Part 2 must meet all of the following
        inclusion criteria to be eligible:

          -  Histopathologically confirmed diagnosis of metastatic or unresectable malignant
             melanoma. Ocular melanoma participants are not eligible.

          -  Participants must have received prior treatment with anti-PD-1 or anti-PD-L1 therapy
             (alone or as part of a combination) in the advanced or metastatic setting and had
             documented progression per RECIST. Participants must have received at least 4 doses of
             anti-PD-1 or anti-PD-L1 therapy.

          -  Participants must have measurable disease by RECIST Version 1.1.

          -  Capable of understanding and complying with protocol requirements.

          -  A life expectancy of greater than 24 weeks at Screening.

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.

          -  Most recent laboratory values (within 3 weeks prior to Week 1 Day 1) meet the
             following standards:

               1. Bone marrow function: neutrophil count greater than or equal to (>/=) 1,000/cubic
                  millimeter (mm^3), platelet count >/=75,000/mm^3 and hemoglobin concentration >/=
                  8.0 grams per deciliter (g/dL).

               2. Liver function: total bilirubin less than or equal to (<=) 1.5 times the upper
                  limit of normal (ULN) of each institution, aspartate aminotransferase and alanine
                  aminotransferase <=3 times the ULN range of each institution.

               3. Lactate dehydrogenase (LDH) <=2.0 times the ULN range of each institution.

               4. Renal function: serum creatinine <=1.5 times the ULN range of each institution.

          -  The participant must sign a written informed consent form prior to the initiation of
             any study procedures. Adult participants unable to provide written informed consent on
             their own behalf will not be eligible for the study.

        Exclusion Criteria:

          -  Pregnant or breast feeding

          -  Received investigational therapy (that is, small molecule or biologic) within 30 days
             prior to the start of CMP-001 dosing on Week 1 Day 1. However, if an investigational
             drug has a short half-life, a reduced wash out period may be acceptable upon
             permission given by the Sponsor.

          -  Received treatment with anti- cytotoxic T-lymphocyte-associated protein 4
             (anti-CTLA-4) antibody within 30 days prior to the start of CMP-001 dosing on Week 1
             Day 1.

          -  Known infection with human immunodeficiency virus (HIV), hepatitis B virus (HBV) or
             hepatitis C virus (HCV).

          -  Developed autoimmune disorders of Grade 4 while on prior immunotherapy. Participants
             who developed autoimmune disorders of Grade <=3 may enroll if the disorder has
             resolved to Grade <=1 and the participant has been off systemic steroids at doses
             greater than (>) 10 milligrams per day (mg/day) for at least 2 weeks.

          -  Require systemic pharmacologic doses of corticosteroids at or above the equivalent of
             10 mg/day prednisone; replacement doses, topical, ophthalmologic and inhalational
             steroids are permitted. Participants who have a history of adrenal insufficiency and
             are receiving greater than 10 mg/day systemic steroids may be eligible but only after
             Sponsor consultation. Participants who are currently receiving steroids at a dose of
             <=10 mg/day do not need to discontinue steroids prior to enrollment.

          -  Active (that is, symptomatic or growing) central nervous system (CNS) metastases.
             Participants with CNS metastases are eligible for the trial if: a) the metastases have
             been treated by surgery and/or radiotherapy; b) the participant is off corticosteroids
             >10 mg/day and is neurologically stable for at least 2 weeks prior to Screening; c)
             brain MRI completed within 3 months of Screening.

          -  Any concurrent uncontrolled illness, including mental illness or substance abuse,
             which in the opinion of the Investigator, would make the participant unable to
             cooperate or participate in the trial.

          -  Severe uncontrolled cardiac disease within 6 months of screening, including but not
             limited to uncontrolled hypertension; unstable angina; myocardial infarction (MI) or
             cerebrovascular accident (CVA).

          -  Requires prohibited treatment that is, non-protocol specified anticancer.
             pharmacotherapy, surgery or conventional radiotherapy for treatment of malignant
             tumor)

          -  Women of child-bearing potential who are unable or unwilling to use an acceptable
             method of contraception.