Study of Proton SBRT and Immunotherapy for Recurrent/Progressive Locoregional or Metastatic Head and Neck Cancer

Inclusion Criteria: * Age ≥18 years old whose multidisciplinary care team has determined that the treatments outlined in the protocol are the treating physicians' equipoised clinical recommendation, the multidisciplinary head \& neck tumor board's recommendation, and that any reasonable alternative treatments have been reviewed with the subject. * Signed written informed consent in accordance with regulatory and institutional guidelines. * Must be willing to comply with scheduled visits, treatment schedule, laboratory testing and other study obligations. Patients must be receiving SOC treatment for recurrent or progressive Head and Neck cancer. Please refer to UCM procedural manual. * Histologically confirmed head and neck squamous cell carcinoma from any of the primary sites: oral cavity, pharynx, larynx, nasopharynx, sinonasal, cutaneous, or unknown head and neck primary. * Subjects with head and neck squamous cell carcinoma that has progressed during chemotherapy with a platinum-based drug or that has recurred or metastasized after platinum-based chemotherapy or in patients with an intolerance to or contraindication for platinum-based chemotherapy will be eligible. * ECOG performance status 0-2 * Subjects enrolled on the METASTATIC ARM must have at least two (≥) lesions: One lesion must be safely amenable to irradiation with stereotactic body radiation therapy per the treating radiation oncologist. Prior radiation to this lesion is allowed if given ≥ 6 months prior. One lesion must be measurable by CT or MRI per iRECIST 1.1 criteria and should be separate from the lesion to be irradiated. If this target lesion has been previously irradiated, there must be documented disease progression after radiation per RECIST 1.1. * Any prior radiotherapy must have been completed at least 3 weeks prior to enrollment. * Adequate bone marrow, hepatic, and renal function based on screening lab values within 35 days prior to beginning immunotherapy: * 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). * Women of childbearing potential must have a negative serum or urine pregnancy test within 10 days prior to beginning immunotherapy. * Women of childbearing potential (WOCBP) must agree to follow instructions for method(s) of contraception from time of enrollment for the duration of treatment with nivolumab and for 6 months after discontinuation of nivolumab. 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 6 months after the last dose of nivolumab. * Ability to complete questionnaire(s) by themselves or with assistance. * Insurance approval or personal pay for SBRT. * Patient may undergo palliative surgery prior to postoperative proton SBRT and remain in the metastatic arm of the study, as long as the patient meets the other aforementioned criteria relating to the metastatic arm. Surgery is allowable for the locoregionally recurrent arm as per the study schema. Exclusion Criteria: * Active brain metastases or leptomeningeal disease. Note: Treated brain metastases (e.g. GammaKnife or surgical resection) are eligible if these have been treated and are without MRI evidence of progression for at least 8 weeks after treatment. MRI must be performed within 35 days prior tobeginning immunotherapy. * Histologically confirmed non-squamous histologies including salivary gland or other non-squamous histologies (e.g. mucosal melanoma) are not allowed; exception WHO Type I-III nasopharynx, which are allowed. * Subjects with active autoimmune disease or on steroid therapy of \>10 mg/day prednisone or equivalent. * Subjects who have undergone bone marrow or solid organ transplantation. * Known HIV, hepatitis B or C infection. * Treatment with chemotherapy, radiation therapy or immunotherapy including investigational agents within 25 days of beginning immunotherapy. * Women that are breastfeeding or pregnant. * Any concurrent chemotherapy, hormonal therapy, immunotherapy, or investigational therapy apart from the prescribed treatment per protocol. * Other active non-head and neck malignancy \<1 year prior to registration. If there is a history of prior distinct malignancy, they must not be receiving chemotherapy, radiotherapy, or immunotherapy for their other disease at the time of protocol enrollment. Exceptions include: Non-melanotic skin cancer and carcinoma in situ of the cervix.