Study of Pembrolizumab and Concurrent Radiation in Patients With Previously Treated Carcinoma of Unknown Primary

Inclusion Criteria: * Written informed consent and HIPAA authorization for release of personal health information prior to registration. NOTE: HIPAA authorization may be included in the informed consent or obtained separately. * Age ≥ 18 years at the time of consent. * Eastern Cooperative Oncology Group (ECOG) Performance Status of ≤ 2 within 28 days prior to registration. * Archival tissue must be available and identified during screening and shipped prior to Day -21. If archival tissue is not available and the subject is not undergoing a standard of care biopsy, the subject must undergo a research biopsy to obtain fresh tissue prior to start of treatment. * Carcinoma of unknown primary after the following diagnostic procedures have been performed if clinically indicated and are unrevealing of the primary site: * Complete history and clinically appropriate physical * CT scan of chest, abdomen, and pelvis * Directed evaluation of symptomatic areas * Mammogram in women * Colonoscopy in patients with liver metastasis or an elevated CEA * Direct pathologic comparison with prior tumor specimens, where possible, even if prior tumor is early-stage or clinically remote from current disease NOTE: Immunohistochemical stains will be performed according to institutional standards. If a primary carcinoma is identified, the patient should undergo treatment as appropriate for that primary tumor and not be enrolled in the study. The above diagnostic workup does not need to be performed if: (1) it was previously completed at the time of original diagnosis or (2) the investigator does not believe the workup has clinical utility at the current time, given that the patient has received interval therapy. * Histologic confirmation of metastatic adenocarcinoma, poorly differentiated non-small cell carcinoma, or poorly differentiated squamous carcinoma. NOTE: Pathology consultation at Mayo Clinic is recommended if clinically indicated. One scenario is where unknown primary is the most likely diagnosis but immunostains show relatively site-specific marker staining (e.g., CD45, TTF1, chromogranin, GATA3, PAX8, PSA, melanocytic markers). Information provided for pathology consultation should include recent H\&P and imaging reports. * If and when available, submission of genomic sequencing and expression profiling results is mandatory. Results of testing are not required prior to treatment. * At least one measurable lesion (per RECIST 1.1) outside the planned RT fields. * Stable or progressive disease after, or was unable to tolerate, at least one line of prior anticancer therapy for this disease. NOTE: For patients with stable disease, it is strongly encouraged to confirm the presence of active disease (eg, demonstrating 18F-2-fluoro-2-deoxy-D-glucose fluorodeoxyglucose (FDG) avidity via PET or repeat biopsy). * Radiation oncology consultation at enrolling site ≤ 56 days prior to registration to confirm at least two metastatic lesions which are targetable by RT at doses and schedule prescribed in this study and which reside in non-overlapping RT fields. * Demonstrate adequate organ function as defined in the table below. All screening labs to be obtained within 28 days prior to registration. * Hematological * Absolute Neutrophil Count (ANC) ≥ 900 K/mm3 * Hemoglobin (Hgb) ≥ 8.5 g/dL without transfusion or EPO dependency (≤ 7 days prior to assessment) * Platelets ≥ 90,000 / mcL * Renal ---Creatinine OR Calculated creatinine clearance: ≤ 1.5 X upper limit of normal (ULN) OR ≥ 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN * Hepatic * Bilirubin Total bilirubin ≤ 1.5 X ULN OR Direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 ULN OR total bilirubin ≤2 X ULN if liver metastases are present * Aspartate aminotransferase (AST) and Alanine aminotransferase (ALT) ≤ 2.5 X ULN OR ≤ 5 X ULN for subjects with liver metastases * Albumin \> 2.5 g/dL * Females of childbearing potential must have a negative serum pregnancy test within 72 hours prior to registration. NOTE: If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. NOTE: breast milk cannot be stored for future use while the mother is being treated on study * Females of childbearing potential and males must be willing to abstain from heterosexual activity (abstinence) or use effective methods of contraception as described in the protocol from the time of informed consent until 120 days after treatment discontinuation. NOTE: Females are considered of child bearing potential unless they are surgically sterile (have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or they are naturally postmenopausal for at least 12 consecutive months * Willingness to return to the enrolling institution for follow up * Willingness to provide tissue and blood samples for correlative research purposes Exclusion Criteria: * Prior radiation to an area of the body which, if included in the current radiation field, poses an unacceptably high risk of toxicity in the opinion of the investigator. NOTE: A prior field that overlaps with the current field, by itself, does not exclude the patient. * Any of the following --Melanoma. NOTE: Positive tumor staining for S-100 or HMB45 alone does not exclude patients. ---If immunostains are performed, and any of the below tests are positive: * Hematologic CD45+ (others such as CD2, CD20, CD30, CD43 also suggest hematologic origin) * Lung or thyroid origin (Thyroid Transcription Factor \[TTF-1\]). NOTE: Patients with biopsy proven TTF-1 positive tumor who do not have clinical evidence for either lung or thyroid cancer (e.g. a dominant lung mass) are still eligible. * Progressed on 4 or more lines of prior chemotherapy for this cancer. NOTE: Bisphosphonates and neoadjuvant/adjuvant anticancer therapies (including locally directed therapies) do not count as a line of therapy with regard to this exclusion criteria. * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens. * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment. * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. * Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. NOTE: Inhaled steroids or steroid injections for joint disease are allowed. * Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Prior severe allergic reactions to a monoclonal antibody or hypersensitivity to pembrolizumab or any of its excipients. * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier. * Other active malignancy which requires current treatment and which in the opinion of the site investigator is likely to interfere with evaluation of disease assessment. --NOTE: Continuation of hormonal therapies is allowed. * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability. * Major surgery ≤ 4 weeks from registration. NOTE: Diagnostic laparoscopy (without other intervention) and/or biopsies (needle aspirate, core biopsy, open biopsy, etc…) are not considered major surgery. If subject received surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. * Uncontrolled intercurrent illness which in the opinion of the investigator poses unacceptably high risk when combined with study treatment, including but not limited to the following: * Symptomatic congestive heart failure * Unstable angina pectoris * Severely impaired lung function * Known history of active TB (Bacillus Tuberculosis) * Uncontrolled diabetes as defined by fasting serum glucose \>1.5 x ULN ---(NOTE: Optimal glycemic control should be achieved before starting trial therapy.) * Significant underlying liver disease such as cirrhosis or severe hepatic impairment * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Has an active infection requiring systemic therapy. * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. * For patients in whom planned RT fields will include the heart, any of the following heart conditions, if in the opinion of the investigator they pose unacceptably high risk when combined with study treatment: * Prior symptomatic congestive heart failure * Documented myocardial infarction ≤6 months prior to registration (pretreatment ECG evidence of infarct only will not exclude patients) * Prior significant ventricular arrhythmia requiring medication * Prior 2nd or 3rd degree heart block or other types of clinically significant conduction delay ≤ 6 months prior to registration * Clinically significant pericardial disease (including pericardial effusion, pericarditis) or cardiac valvular disease ≤12 months prior to registration NOTE: As part of history and physical, all patients must be assessed for signs or symptoms of cardiac disease, or for prior history of cardiac disease. These conditions include but are not limited to diseases related to cardiac valves, pericardium, myocardium, atrioventricular delays or arrhythmias. It is strongly recommended that signs or symptoms of potentially clinically significant disease be evaluated with comprehensive cardiac echo. * For patients in whom planned RT fields during the study will include the chest, any of the following, if in the opinion of the site investigator they pose unacceptably high risk when combined with study treatment: * Prior fistula within thorax, including bronchoalveolar or esophageal. * Respiratory condition that required oxygen supplementation ≤ 3 months prior to registration * Clinically significant pulmonary hypertension ≤ 12 months prior to registration * Pneumonia requiring treatment ≤ 1 month prior to registration * Pulmonary embolism requiring treatment ≤ 6 months prior to registration * Pleural effusion requiring drainage ≤ 12 months prior to registration * Has known history of, or any evidence of active, non-infectious pneumonitis * Currently uncontrolled hyper/hypothyroidism or hyper/hypocortisolism if in the opinion of the investigator they pose unacceptably high risk when combined with study treatment * Received live vaccine ≤ 30 days prior to registration. NOTE: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed. * History of organ or stem cell transplantation