Pembrolizumab With or Without Radiation in Patients With Recurrent or Metastatic Adenoid Cystic Carcinoma

Inclusion Criteria: * Participants must have histologically confirmed adenoid cystic carcinoma with evidence of recurrent or metastatic disease not amenable to potentially curative surgery or radiotherapy. * Participants must have at least two RECIST v1.1 measurable non-CNS based lesions. Palliative radiation must be indicated for at least one of these lesions, and this lesion must be a candidate for radiation to a dose of 30 Gy of radiation over 5 fractions as deemed by a treating radiation oncologist. Documentation of volume and prescription isodose line will be collected. Re-irradiation of a previously treated lesion is not allowed. One lesion must be in a location where it will not be incorporated into the radiation fields so systemic response can be assessed. However, inclusion of patients with more than 10 measurable lesions is strongly discouraged and all patients must have life expectancy \> 6 months. * Participants must agree to undergo a research biopsy, if tumor is safely accessible, at baseline and after 2 cycles of pembrolizumab. Participants can be exempt if archival tumor tissue has been collected within 12 months of study enrollment that the Principal Investigator deems it appropriate/sufficient for analysis on this protocol. Biopsy of a lesion outside of the potential radiation treatment field is preferred to maintain consistency across cohorts. * Participants must have archival tissue from the primary tumor or metastases available for correlative studies. Either a paraffin block or twenty unstained slides are acceptable. If twenty slides are not available, a lesser amount may be acceptable after discussion with the Principal Investigator. * Prior systemic therapy: At least 2 weeks must have elapsed since the end of prior chemotherapy, biological agents (4 weeks for anti-cancer monoclonal antibody containing regimens) or any investigational drug product, with adequate recovery of treatment-related toxicity to NCI CTCAE Version 4.0 grade ≤1 (or tolerable grade 2) or back to baseline (except for alopecia or neuropathy). Any number of prior therapies for recurrent/metastatic ACC are allowed, with the exception of previous treatment with PD-1 pathway inhibitors. * Prior radiation therapy: At least 3 weeks must have elapsed from prior radiation therapy. The prior site of radiotherapy must be documented as reirradiation of the same site is not allowed in this protocol. * Be ≥ 18 years of age on day of signing informed consent. * Have a performance status of 0 or 1 on the ECOG Performance Scale (see Appendix A). * Participants must have documentation of a new or progressive lesion on a radiologic imaging study performed within 12 months prior to study enrollment (progression of disease over any interval is allowed) and/or new/worsening disease related symptoms within 12 months prior to study enrollment. This assessment is performed by the treating investigator. Evidence of progression by RECIST criteria is not required. * Demonstrate adequate organ function as defined in Table 1, all screening labs should be performed within 10 days of treatment initiation. Table 1 Adequate Organ Function Laboratory Values System Laboratory Value * Hematological * Absolute neutrophil count (ANC) ≥1,500 /mcL * Platelets ≥100,000 / mcL * Hemoglobin ≥9 g/dL or ≥5.6 mmol/L without transfusion or EPO dependency (within 7 days of assessment) * Renal * Serum creatinine OR Measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCl) ≤1.5 X upper limit of normal (ULN) OR ≥60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN * Hepatic * Serum total bilirubin ≤ 1.5 X ULN OR Direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 ULN * AST (SGOT) and ALT (SGPT) ≤ 2.5 X ULN OR ≤ 5 X ULN for subjects with liver metastases * Albumin \>2.5 mg/dL * Coagulation * International Normalized Ratio (INR) or Prothrombin Time (PT) * Activated Partial Thromboplastin Time (aPTT) ≤1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants ≤1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Creatinine clearance should be calculated per institutional standard. * Baseline tumor measurements must be documented from tests within 28 days of study entry. Other non-laboratory tests must be performed within 28 days of study entry. * Female subjects of childbearing potential should have a negative urine or serum pregnancy within 7 days prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Female and male subjects of childbearing potential must agree to use an adequate method of contraception, as outlined in section 5.6, prior to study entry, for the duration of study participation, and 4 months after completion of pembrolizumab administration. Contraception is required starting with the first dose of study medication through 120 days after the last dose of study medication. * Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. * Be willing and able to provide written informed consent for the trial. Exclusion Criteria: * Metastatic disease impinging on the spinal cord or threatening spinal cord compression. Patients that have had previous treatment of disease with impinging on the cord with either surgery or radiotherapy with clinical or radiographic evidence of response or stability are eligible. * Surgical fixation of bone lesion to be irradiated is required and indicated to provide mechanical stability. * Participant 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), have no evidence of new or enlarging brain metastases, and are not using steroids for the purposes of treating brain metastasis induced edema for at least 7 days prior to trial treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability, because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Prior treatment with PD-1 or PD-L1 inhibitor * Concurrent administration of other cancer specific therapy or investigational agents during the course of this study is not allowed. * 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 a known history of active TB (Bacillus Tuberculosis) * History of allergic reactions or hypersensitivity to pembrolizumab or any of its excipients. * Uncontrolled intercurrent illness including but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer. * Has known history of, or any evidence of active, non-infectious pneumonitis. * Has an active infection requiring systemic therapy. * 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 (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * 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. * Subjects who are 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. Pregnant women are excluded from this study because immunotherapy has the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk of adverse events in nursing infants secondary to treatment of the mother with immunotherapy, breastfeeding should be discontinued if the mother is treated on this protocol. Women who could potentially become pregnant while undergoing treatment on this protocol must be willing to use 2 methods of contraception. * Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). * Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Has received a live vaccine within 30 days of planned start of study therapy.