Phase 2 Trial of Ipilimumab and Nivolumab in Nasopharyngeal Carcinoma

Inclusion Criteria: * Patients with recurrent and/or metastatic nasopharyngeal carcinoma, which is not feasible for curative therapy. * Patients must have histologically or cytologically confirmed NPC with Epstein-Barr Encoded RNA (EBER) positive tumour cells and/or elevated serum EBV DNA viral titres. * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>20 mm with conventional techniques or as \>10 mm with spiral CT scan, MRI, or calipers by clinical exam. * No more than 1 line of previous chemotherapy and/or targeted therapy or patients who do not tolerate chemotherapy. Pts who progress within 1 year of chemoradiation for locally advanced disease are allowed on study. * Age \> 21. In Taiwan, patients with who are older than 20 years old are eligible * Life expectancy \> 3 months * Eastern Cooperative Oncology Group (ECOG) 0-1 * Patients must have normal organ and marrow function as defined below: * White Blood Cells (WBC) ≥ 2000/μL * Neutrophils ≥ 1500/μL * Platelets ≥ 100 x10\*\*3/μL * Hemoglobin \> 9.0 g/dL * Serum creatinine ≤ 1.5 x Upper Limit of Normal (ULN) or creatinine clearance (CrCl) ≥ 40 mL/min (if using the Cockcroft-Gault formula below): * 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) * Aspartate Transaminase/Alanine Transaminase (AST/ALT) ≤ 3 x ULN * Total Bilirubin ≤ 1.5 x ULN (except subjects with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dL) * Measurable levels of circulating EBV DNA * Women of childbearing potential (WOCBP) must use appropriate method(s) of contraception. WOCBP should use an adequate method to avoid pregnancy for 23 weeks (30 days plus the time required for nivolumab/ipilimumab to undergo five half-lives) after the last dose of investigational drug * Women of childbearing potential must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of nivolumab/ipilimumab * Women must not be breastfeeding * 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/ipilimumab 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 (ie, who are postmenopausal or surgically sterile as well as azoospermic men do not require contraception * Ability to understand and the willingness to sign a written informed consent document. * Any surgery must be more than 28 days before start of study drug and any surgical wounds must be completely healed Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. * Patients who are receiving any other investigational agents. * Patients are excluded if they have active brain metastases or leptomeningeal metastases. Subjects with brain metastases are eligible if metastases have been treated and there is no magnetic resonance imaging (MRI) evidence of progression for \[lowest minimum is 4 weeks or more\] after treatment is complete and within 28 days prior to the first dose of IO administration. There must also be no requirement for immunosuppressive doses of systemic corticosteroids (\> 10 mg/day prednisone equivalents) for at least 2 weeks prior to study drug administration. * Patients should be excluded if they are positive test for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to nivolumab or ipilimumab. * Prior use of anti-PD1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-CTLA-4 antibody, or any drug specifically targeted T-cell costimulatory checkpoint pathways * 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. * Pregnant women are excluded from this study because ipilimumab has the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with nivolumab or ipilimumab, breastfeeding should be discontinued if the mother is treated with nivolumab or ipilimumab. * Patients should be excluded if they have known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) * 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 * Patients should be excluded if they have a condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. * Patient should be excluded if they have history or active interstitial lung disease (pneumonitis). * Prior organ allograft or allogeneic bone marrow transplantation * Allergies and Adverse Drug Reaction * History of allergy to study drug components * History of severe hypersensitivity reaction to any monoclonal antibody * Prisoners or subjects who are involuntarily incarcerated * Subjects who are compulsorily detained for treatment of either a psychiatric or physical (eg, infectious disease) illness * Inability to comply with restrictions and prohibited activities/treatments in this study * Subjects with concomitant second malignancies (except adequately treated non-melanomatous skin cancers, in situ cervical cancers, localized prostate cancer or in situ breast cancer) are excluded unless a complete remission was achieved at least 3 years prior to study entry and no additional therapy is required or anticipated to be required