Inclusion Criteria:  Subjects enrolled in the study must meet all of the following inclusion criteria to be eligible.  Histopathologically-confirmed diagnosis of cancer that is metastatic or unresectable at Screening.  Subjects with metastatic or locally and/or regionally advanced unresectable CSCC.  Note 1: CSCC subjects without radiographically measurable disease are not excluded if there is at least 1 lesion ≥ 10 mm in at least 1 dimension documented by color photography. Note 2: Subjects with tumors that arise in the setting of chronic inflammation (Marjolin's ulcer) such as chronic wounds and/or scars are excluded. Cohort A1: Subjects who have not received prior systemic therapy for CSCC. Cohort A2: Subjects who have progressed while receiving a PD-1-blocking antibody or within 3 months of discontinuation. PD-1-blocking antibody treatment may have been administered in the adjuvant and/or neoadjuvant and/or metastatic setting. The PD-1-blocking antibody must have been the most recent therapy received.  Subjects with metastatic or locally and/or regionally advanced unresectable MCC.  Note: MCC subjects without radiographically measurable disease are not excluded if there is at least 1 lesion ≥ 10 mm in at least 1 dimension documented by color photography. Cohort B1: Subjects who had not received prior systemic therapy for MCC. Cohort B2: Subjects who have progressed while receiving PD-1-blocking antibody(ies) or within 3 months of discontinuation. PD-1-blocking antibody treatment may have been administered in the adjuvant and/or neoadjuvant and/or metastatic setting. The PD-1-blocking antibody must have been the most recent therapy received.  Previously treated subjects with advanced or metastatic TNBC must have disease that is HER2-negative, estrogen and progesterone receptor-negative, or < 5% expression based on American Society of Clinical Oncology/College of American Pathologists guidelines.  Patients with disease recurrence or progression following neoadjuvant or adjuvant therapy are eligible. Patients with advanced or metastatic disease may have up to 5 lines of systemic therapy. Cohort C1: Subjects who had not received prior therapy with iCPIs. Cohort C2: Subjects who had received prior treatment with a PD-1-blocking antibody.  Subjects enrolled in Cohorts A2, B2, and C2 must have PD on or within 3 months of discontinuation of prior PD-1-blocking antibody therapy, either as a single agent or in combination with a standard or an investigational therapy. Subjects who progressed on/within 3 months of adjuvant or neoadjuvant therapy with iCPI will be allowed in Cohorts A2, B2, and C2.  Measurable disease, as defined by RECIST v1.1 and all of the following:  At least 1 accessible lesion amenable to repeated IT injection. A previously irradiated lesion may be used as a target lesion if subsequent disease progression in that lesion (at least 20% increase in dimensions with a 5 mm absolute increase) was documented. Able to provide tissue from a core or excisional/incisional biopsy (fine needle aspirate is not sufficient). A newly obtained biopsy (within 90 days before the start of study treatment) is preferred but an archival sample is acceptable if no intervening therapy was received.  Adequate organ function based on most recent laboratory values within 3 weeks before first dose of study treatment on Week 1 Day 1 (W1D1):  Bone marrow function:  neutrophil count ≥ 1500/mm3 platelet count ≥ 100,000/mm3 hemoglobin concentration ≥ 9 g/dL  Liver function:  total bilirubin ≤ 1.5 times the upper limit of normal (ULN) with the following exception: subjects with Gilbert Disease total serum bilirubin ≤ 3 times ULN aspartate aminotransferase and alanine aminotransferase ≤ 3 times the ULN  Renal function: estimated (Cockcroft-Gault) or measured creatinine clearance  ≥ 30 mL/min  Coagulation:  International normalized ratio or prothrombin time (PT) ≤ 1.5 times ULN unless subject is receiving anticoagulant therapy, as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants. Activated partial thromboplastin time or PTT ≤ 1.5 times ULN unless subject is receiving anticoagulant therapy, as long as PT or PTT is within therapeutic range of intended use of anticoagulants. Age ≥ 18 years at time of consent. Eastern Cooperative Oncology Group Performance Status of 0 to 1 at Screening. Capable of understanding and complying with protocol requirements. Women of childbearing potential must have negative serum pregnancy test during Screening and be willing to use an adequate method of contraception from the time of consent until at least 150 days after last dose of study treatment. Able and willing to provide written informed consent and to follow study instructions.  Subjects unable to provide written informed consent on their own behalf will not be eligible for the study.  Exclusion Criteria:  Subjects presenting with any of the following will not qualify for entry into the study:  Received radiation therapy (or other nonsystemic therapy) within 2 weeks before first dose of study treatment on W1D1. Subjects should have recovered (ie, Grade ≤ 1 or at baseline) from radiation-related toxicities. Treatment with complementary medications (eg, herbal supplements or traditional Chinese medicines) to treat the disease under study within 2 weeks prior to start of study treatment or at any time during the treatment phase of the study.  Received systemic pharmacologic doses of corticosteroids > 10 mg/day prednisone within 30 days before first dose of study treatment on W1D1.  Subjects who are currently receiving steroids at a prednisone-equivalent dose of  ≤ 10 mg/day do not need to discontinue steroids prior to enrollment.  Replacement doses, topical, ophthalmologic, and inhalational steroids are permitted. Stress-dose corticosteroids will be required in subjects with adrenal insufficiency. History of immune-mediated AE leading to permanent discontinuation due to prior PD-1-blocking antibody. Not fully recovered from AEs due to prior treatment (to Grade 1 or less, per CTCAE), with the exception of persistent vitiligo, alopecia, hypothyroidism, or diabetes mellitus, and adrenal and/or pituitary insufficiency, due to prior treatment. Note: Subjects previously treated with a CTLA-4-blocking antibody, subjects receiving corticosteroids with daily doses >5mg and ≤10mg of prednisone equivalent for >2 weeks, and subjects with clinical symptoms and/or laboratory findings suggesting risk for adrenal insufficiency should undergo diagnostic tests for adrenal insufficiency via local laboratory. Active pneumonitis or history of noninfectious pneumonitis that required steroids, or history of interstitial lung disease. Severe uncontrolled cardiac disease within 6 months of Screening, including but not limited to poorly controlled hypertension, unstable angina, myocardial infarction, congestive heart failure (New York Heart Association Class II or greater), pericarditis within the previous 6 months, cerebrovascular accident, or implanted or continuous use of a pacemaker or defibrillator. Known history of immunodeficiency. Known additional malignancy that is progressing or required active treatment within the past 3 years. Exceptions include cancers that have undergone potentially curative therapy, e.g. basal cell carcinoma of the skin, squamous cell carcinoma of the skin that has undergone potentially curative therapy, curatively treated localized prostate cancer with prostate-specific antigen level below 4.0 ng/mL, in situ cervical cancer on biopsy or a squamous intraepithelial lesion on Papanicolaou smear, and thyroid cancer (except anaplastic),in situ breast cancer and adjuvant hormonal therapy for breast cancer > 3 years from curative-intent surgical resection. Active autoimmune disease that required systemic treatment in past 2 years; replacement therapy is not considered a form of systemic treatment. Untreated, symptomatic, or enlarging central nervous system metastases or carcinomatous meningitis (including leptomeningeal metastases from solid tumors). Prior allogenic tissue/solid organ transplant. Active infection requiring systemic therapy. Known or suspected active infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Known or suspected infection with human immunodeficiency virus, hepatitis B virus, or hepatitis C virus (testing is not required unless suspected). Received a live virus/attenuated vaccination within 30 days before first dose of study treatment on W1D1. Received blood products (including platelets or red blood cells) or colony stimulating factors (including granulocyte colony stimulating factor, granulocyte/macrophage colony stimulating factor, or recombinant erythropoietin) within 3 weeks before the W1D1 visit. History of permanent discontinuation of cemiplimab-rwlc due to infusion reactions. Any concurrent uncontrolled illness, including mental illness or substance abuse, which in the opinion of the Investigator would make the subject unable to cooperate or participate in the study. Participation in another clinical study of an investigational anticancer therapy or device within 30 days before first dose of study treatment on W1D1. Note: Participation in the follow-up phase (receiving no study treatment) of a prior study is allowed. Requires prohibited treatment (ie, non-protocol specified anticancer pharmacotherapy, surgery, or conventional radiotherapy) for treatment of malignant tumor. Has a life expectancy of less than 3 months and/or has rapidly progressing disease (eg, tumor bleeding, uncontrolled tumor pain) in the opinion of the treating Investigator. Received previous CMP-001 treatment. Pregnant or breastfeeding or expecting to conceive children within the projected duration of the study, from the time of consent until at least 150 days after last dose of study treatment.