Study of Avelumab and/or Radiation Therapy in People With Advanced Merkel Cell Carcinoma

Inclusion Criteria: * Biopsy proven Merkel cell carcinoma which is unresectable or metastatic, stage III or IV * Prior first-line treatment with aPD1 monotherapy (defined as at least one dose of pembrolizumab, avelumab, nivolumab, etc.) with evidence of progression of disease ≥10 weeks after starting therapy, in the absence of significant clinical deterioration * Patients with clinical deterioration during aPD1 monotherapy are eligible ≥6 weeks after starting aPD1 therapy * Criteria for clinical deterioration to be determined and agreed upon by treating physician and Principal Investigator * All detectable sites of MCC are amenable to comprehensive ablative radiation therapy in opinion of treating radiation oncologist and principal investigator * ≥18 years of age * Performance status ≤2 on the Eastern Cooperative Oncology Group Performance Scale * Able to provide valid written informed consent * Normal organ and marrow function * Hematologic: Neutrophil count ≥1500/mm\^3, platelet count ≥100,000/mm\^3, hemoglobin ≥9 g/dL * Hepatic: Total bilirubin ≤ 1.5 times the upper limit of normal, unless Gilbert's syndrome; aspartate transaminase and alanine transaminase ≤ 2.5 times the upper limit of normal (in the absence of hepatobiliary metastases); ≤ 3.0 times the upper limit of normal (in the presence of hepatobiliary metastases) * Renal: Estimated creatinine clearance ≥ 30 mL/min according to the Cockcroft-Gault formula. Exclusion Criteria: * Prior systemic therapy …