Screening Trial of Nivolumab With Image Guided, Stereotactic Body Radiotherapy (SBRT) Versus Nivolumab Alone in Patients With Metastatic Head and Neck Squamous Cell Carcinoma (HNSCC)

Inclusion Criteria: * Signed Written Informed Consent * Subjects must have signed and dated an IRB/IEC approved written informed consent form in accordance with regulatory and institutional guidelines. * Subjects must be willing and able to comply with scheduled visits, treatment schedule, laboratory testing, and other study obligations. * Target Population * Males and females ≥ 18 years of age * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2. * Histologically confirmed metastatic HNSCC, including nasopharynx WHO Type I-III histologies; patients can have simultaneous loco-regional disease. Central biopsy review at MSKCC is not required. * Subjects must have at least two lesions: * At least one lesion must be safely amenable to irradiation and likely to meet criteria delineated in Section 9.2.1 in the judgment of the treating radiation oncologist. This can be a lesion that was previously irradiated as long as prior radiation was at least 6 months prior to projected first fraction of SBRT and as long as reirradiation dose constraints as outlined in appendix are being met. * A separate, not-to-be-irradiated lesion measurable by CT or MRI per RECIST 1.1 criteria. * A formalin fixed, paraffin-embedded (FFPE) tumor tissue block or a minimum of 3 unstained slides of tumor sample obtained via excisional, incisional, or core needle biopsy from a metastatic or loco-regionally recurrent lesion. A new baseline biopsy does not need to be obtained for study purposes. If 3 unstained are unavailable from a metastatic or loco-regionally recurrent lesion, with permission of the PI, FFPE tumor tissue from the primary disease site at the time of original diagnosis is acceptable. * For oropharynx or nasopharynx primary lesions, documentation of viral status is required (e.g. high risk HPV sub-type PCR, p16 IHC, HPV ISH, EBER, etc). Tests done on primary tumor specimens from date of initial diagnosis at outside institutions are sufficient to meet this criterion * Prior palliative or curative radiotherapy must be completed at least 14 days prior to randomization. * Immunosuppressive doses of systemic medication, such as steroids or absorbed topical steroids (doses \>10mg/day prednisone or equivalent) must be discontinued at least 14 days prior to Nivolumab administration. * Screening laboratory values must meet the following criteria (using CTCAE v4.0) and should be obtained within 28 days prior to randomization: * WBC ≥ 2 K/microliter * Neutrophils ≥ 1.5 ;K/microliter * Platelets ≥ 100 K/microliter * Hemoglobin ≥ 9.0 g/deciliter * Serum Creatinine ≤ 1.5 x ULN or creatinine clearance \> 40ml/min using the Cockcroft-Gault formula. * Female CrCl = (140 - age in years) x weight in kg x 0.85 72 x serum creatinine in mg/dL * Male CrCl = (140 - age in years) x weight in kg x 1.00 72 x serum creatinine in mg/dL * AST/ALT ≤ 3 x ULN * Total bilirubin \<1.5 x ULN (except subjects with Gilbert Syndrome who can have total bilirubin \<3.0 mg/deciliter) Calcium levels must be normalized and maintained within normal limits for study entry and while on treatment. * Subjects with an initial magnesium \<0.5 mmol/liter (1.2 mg/deciliter) may receive corrective magnesium supplementation but should continue to receive either prophylactic weekly infusion of magnesium and/or oral magnesium supplementation. * Subjects must have a resting baseline O2 saturation by pulse oximetry of \>=92% at rest. * Reproductive Status * Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 28 days prior to randomization. * Women must not be breastfeeding * Women of childbearing potential must agree to follow instructions for method(s) of contraception from time of enrollment for the duration of treatment with Nivolumab plus 5 half- lives plus 30 days for a total of 23 weeks post treatment completion. * Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year. Men receiving Nivolumab and who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 31 weeks after the last dose of investigational product. * Women who are not of childbearing potential (i.e., who are postmenopausal or surgically sterile as well as azoospermic men do not require contraception. * Azoospermic males and women of childbearing potential who are continuously not heterosexually active are exempt from contraceptive requirements. However, they still must have a pregnancy test. * Insurance Approval * Insurance approval for SBRT should be obtained prior to randomization Exclusion Criteria: * Target Disease Exceptions * Active brain metastases (untreated brain metastases or growth on imaging as defined below) or leptomeningeal disease are not allowed. Subjects with brain metastases are eligible if these have been treated and there is no MRI (or CT if MRI contraindicated) evidence of progression for at least 8 weeks after treatment for these metastases is complete and within 28 days prior to first study treatment. * Histologically confirmed non-squamous histologies are not allowed; an exception is made for WHO Type I-III nasopharynx histologies. * Medical History and Concurrent Diseases: * Any medical disorder that, in the opinion of the investigator, might increase the risk associated with study participation or interferes with the interpretation of study results. * Prior active malignancy within the previous 3 years except for locally curable cancers such as basal or squamous skin cancer, superficial bladder, low risk prostate cancer, breast, or cervix cancer. If other prior malignancy was active within prior 3 years, enrollment requires approval of a principal investigator. * Patients should be excluded if they have an active, known or suspected autoimmune disease. Subjects are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger * Subjects with a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration should be excluded. Inhaled or topical steroids and adrenal replacement doses \>10mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. * As there is potential for hepatic toxicity with Nivolumab, drugs with a predisposition to hepatoxicity should be used with caution in patients treated with Nivolumab-containing regimen. * Prior treatment with an anti-PD-1, anti-PD-L1, or anti-PD-L2 antibody. * NB-patients who have received prior anti-CTLA-4 antibody therapy are eligible assuming such therapy was discontinued within 28 days of enrollment. * Treatment with any chemotherapy, radiation therapy, biologics for cancer, or investigational therapy within 14 days of randomization. * Physical and Laboratory Test Findings * Positive test for hepatitis B virus surface antigen or hepatitis C virus ribonucleic acid indicating acute or chronic infection. * Known history of testing positive for HIV or known AIDS. * Any grade 4 laboratory abnormalities. * Allergies and Adverse Drug Reaction * History of allergy to Nivolumab components * History of severe hypersensitivity reaction to any monoclonal antibody. * Prohibited or Restricted Treatments * The following medications are prohibited during the study: * Immunosuppressive agents (except to treat a drug-related adverse event). * Systemic corticosteroids \> 10 mg daily prednisone equivalent save for exclusion outlined in the below paragraphs. * Any concurrent chemotherapy, hormonal therapy, immunotherapy, or investigational agents for treatment of cancer.