Avelumab in Participants With Merkel Cell Carcinoma (JAVELIN Merkel 200)

Inclusion Criteria:

* Signed written informed consent
* Age 18 years and above
* Histologically proven MCC
* Participants must have received at least 1 line of chemotherapy for metastatic MCC and must have progressed after the most recent line of chemotherapy
* For Part B - Participants must not have received any prior systemic treatment for metastatic MCC. Prior chemotherapy treatment in the adjuvant setting (no clinically detectable disease; no metastatic disease) is allowable if the end of treatment occurred at least 6 months prior to study start)
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1
* Disease must be measurable with at least 1 uni-dimensional measurable lesion by RECIST Version 1.1 (including skin lesions)
* Adequate hematological, hepatic and renal function (renal function considered adequate as per protocol definition)
* Highly effective contraception for both male and female participants, if the risk of conception exists
* Fresh Biopsy or Archival Tumor Tissue
* Estimated life expectancy of more than 12 weeks

Exclusion Criteria:

* Participation in another interventional clinical trial within the past 30 days (participation in observational studies is permitted)
* Concurrent treatment with a non permitted drug
* Prior therapy with any antibody/drug targeting T-cell coregulatory proteins (immune checkpoints) such as antiprogrammed death 1 (PD-1), anti-PD-L1, or anticytotoxic T-lymphocyte antigen-4 (CTLA-4) antibody; for Part B, the Investigator must consult with the Medical Monitor and consider other co-regulatory targets such as 4-1BB
* Concurrent anticancer treatment (for example, cytoreductive therapy, radiotherapy \[with the exception of palliative bone-directed radiotherapy, or radiotherapy administered on non-target superficial lesions\], immune therapy, or cytokine therapy except for erythropoietin). Radiotherapy administered to superficial lesions is not allowed if such lesions are considered target lesions in the efficacy evaluation or may influence the efficacy evaluation of the investigational agent
* Major surgery for any reason, except diagnostic biopsy, within 4 weeks and/or if the participant has not fully recovered from the surgery within 4 weeks
* Concurrent systemic therapy with steroids or other immunosuppressive agents, or use of any investigational drug within 28 days before the start of trial treatment. Short-term administration of systemic steroids (that is, for allergic reactions or the management of immune-related adverse events \[irAE\]) while on study is allowed. Also, participants requiring hormone replacement with corticosteroids for adrenal insufficiency are eligible if the steroids are administered only for the purpose of hormonal replacement and at doses \<= 10 mg or equivalent prednisone per day. Note: Participants receiving bisphosphonate or denosumab are eligible.
* Participants with active central nervous system (CNS) metastases are excluded. Participants with a history of treated CNS metastases (by surgery or radiation therapy) are not eligible unless they have fully recovered from treatment, demonstrated no progression for at least 2 months, and do not require continued steroid therapy
* Previous malignant disease (other than MCC) within the last 5 years with the exception of basal or squamous cell carcinoma of the skin and for Part A cervical carcinoma in situ or for Part B carcinoma in situ (skin, bladder, cervical, colorectal, breast or low grade prostatic intraepithelial neoplasia or Grade 1 prostate cancer)
* Prior organ transplantation, including allogeneic stem-cell transplantation
* Part A: Known history of testing positive for HIV or known acquired immunodeficiency syndrome (AIDS) or any positive test for hepatitis B virus or hepatitis C virus indicating acute or chronic infection. For Part B, known history of testing positive for HIV or known AIDS in consultation with the Medical Monitor or HBV or HCV infection at screening (positive HBV surface antigen or HCV RNA if anti- HCV antibody screening test positive).
* Active or history of any autoimmune disease (except for participants with vitiligo) or immunodeficiencies that required treatment with systemic immunosuppressive drugs
* Known severe hypersensitivity reactions to monoclonal antibodies (Grade greater than or equal to (\>=) 3 NCI CTCAE v 4.0), any history of anaphylaxis, or uncontrolled asthma (that is, 3 or more features of partially controlled asthma)
* Persisting toxicity related to prior therapy Grade \> 1 NCI-CTCAE v 4.0; however, sensory neuropathy Grade \<= 2 is acceptable 14. Pregnancy or lactation
* Known alcohol or drug abuse
* Clinically significant (that is, active) cardiovascular disease: cerebral vascular accident / stroke (\< 6 months prior to enrollment), myocardial infarction (\< 6 months prior to enrollment), unstable angina, congestive heart failure (New York Heart Association Classification Class \>= II), or serious cardiac arrhythmia requiring medication
* All other significant diseases (for example, inflammatory bowel disease), which, in the opinion of the Investigator, might impair the participant's tolerance of trial treatment
* Any psychiatric condition that would prohibit the understanding or rendering of informed consent
* Legal incapacity or limited legal capacity
* Non oncology vaccine therapies for prevention of infectious disease (for example, seasonal flu vaccine, human papilloma virus vaccine) within 4 weeks of trial drug administration. Vaccination while on trial is also prohibited except for administration of inactivated vaccines (for example, inactivated seasonal influenza vaccine)