This randomized phase II trial studies how well pembrolizumab with or without stereotactic body radiation therapy works in treating patients with Merkel cell cancer that has spread to other places in the body (advanced). Immunotherapy with monoclonal antibodies, such as pembrolizumab, may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Stereotactic body radiation therapy uses special equipment to position a patient and deliver radiation to tumors with high precision. This method can kill tumor cells with fewer doses over a shorter period and cause less damage to normal tissue. Giving pembrolizumab with stereotactic body radiation therapy may work better in treating patients with Merkel cell cancer.

PRIMARY OBJECTIVE:

I. To describe the progression-free survival (PFS) of stereotactic body radiation therapy (SBRT) + pembrolizumab (MK-3475) compared to pembrolizumab (MK-3475) alone in advanced/metastatic Merkel cell carcinoma (MCC) patients.

SECONDARY OBJECTIVES:

I. To describe the PFS of SBRT + MK-3475 compared to pembrolizumab (MK-3475) alone across Response Evaluation Criteria in Solid Tumors (RECIST) measurable (including both radiated and non-radiated) cancer deposits.

II. To describe the overall response rate of SBRT + pembrolizumab (MK-3475) compared to pembrolizumab(MK-3475) alone in both radiated and in non-radiated deposit(s).

III. To determine the PFS at 6 months of SBRT + pembrolizumab (MK-3475) compared to pembrolizumab (MK-3475) alone across all cancerous deposits by RECIST.

IV. To determine the rate of grade > 3-4 adverse events, by organ system, by Common Terminology Criteria for Adverse Events (CTCAE) version (v) 5.0.

V. To determine the local control of SBRT treated tumors. VI. To calculate delivered radiation dose using cone-beam computed tomography (CT) images collected on the radiation treatment table in the final treatment position.

CORRELATIVE SCIENCE OBJECTIVES:

I. To test the utility of CT-based radiomics to predict radiation-induced pneumonitis and true delivered dose of SBRT based on cone beam collected imaging and diagnostic scans.

II. Biobanking for future correlative science projects.

OUTLINE: Patients are randomized to 1 of 2 groups.

GROUP I: Patients receive pembrolizumab intravenously (IV) over 30 minutes on day 1. Cycles repeat every 21 days for up to 2 years in the absence of disease progression or unacceptable toxicity.

GROUP II: Patients receive pembrolizumab IV over 30 minutes on day 1. Cycles repeat every 21 days for up to 2 years in the absence of disease progression or unacceptable toxicity. Patients also undergo SBRT for 3 doses during cycle 1.

After completion of study treatment, patients are followed up every 6 months for up to 5 years.

Inclusion Criteria:

• Patients must have pathologically (histologically or cytologically) proven diagnosis of MCC by local pathology review

• Have measurable disease based on RECIST 1.1 including at least two cancerous deposits; at least one deposit must be RECIST measurable while at least one deposit must meet criteria for SBRT; non-radiated tumor will be identified prior to randomization on the protocol

• Patients must have advanced or metastatic MCC defined as evidence of distant metastasis(es) on imaging

  • Patients with locoregionally confined disease are not eligible

• No prior immunotherapy for advanced/metastatic MCC

• Patients with known or suspected central nervous system (CNS) metastases, untreated CNS metastases, or with the CNS as the only site of disease are excluded; however, subjects with controlled brain metastases will be allowed to enroll; controlled brain metastases are defined as no radiographic progression for at least 4 weeks following radiation and/or surgical treatment (or 4 weeks of observation if no intervention is clinically indicated), and off of steroids for at least 2 weeks, and no new or progressive neurological signs and symptoms

• Patients having received palliative radiotherapy for extracranial metastasis(es) are eligible as long as there are 2 cancerous deposits that have not received prior radiation therapy (RT) and they meet the following criteria

  • No prior radiation therapy (> 5 Gy) to the metastasis intended to be treated with SBRT

• No history of the following:

  • Autoimmunity requiring systemic immunosuppression within 2 years

  • Patients known to be human immunodeficiency virus (HIV) positive are eligible if they meet the following:

    • CD4 counts >= 350 mm^3
    • Serum HIV viral load of < 25,000 IU/ml

• No other active malignancy that the investigator determines would interfere with the treatment and safety analysis

• Not pregnant and not nursing, because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown; therefore, for women of childbearing potential only, a negative (if your test schedule specifically indicates a urine or serum pregnancy test, add that information at this point) pregnancy test done =< 28 days prior to registration is required

• Eastern Cooperative Oncology Group (ECOG) performance status 0-2

• Absolute neutrophil count (ANC) >= 1,500/mm^3

• Platelet count >= 100,000/mm^3

• Hemoglobin >= 9.0 g/dl

• Total bilirubin =< 2.0 mg/dl

• Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 3.0 x upper limit of normal (ULN)

• Systolic blood pressure (BP) =< 150 mg HG

• Diastolic BP =< 90 mg HG

• Albumin > 3 mg/dl

• Blood urea nitrogen (BUN) =< 30 mg/dl

• Creatinine =< 1.7 mg/dl

• The following imaging workup to document metastases within 45 days prior to study registration are required: CT scans of the chest, abdomen and pelvis with radionuclide bone scan OR whole body (at least skull base to midthigh) positron emission tomography (PET)/CT