Ficlatuzumab and Cetuximab in Recurrent/Metastatic Head and Neck Squamous Cell Carcinoma (HNSCC)

Inclusion Criteria: Each patient must meet all of the following inclusion criteria to be enrolled in the study: * Patients must have histologically confirmed HNSCC, from any primary site. Nasopharyngeal carcinoma, WHO Type I (keratinizing), will be included. Squamous cell carcinoma of unknown primary, clearly related to the head and neck, will be included. * Recurrent/metastatic disease, fulfilling at least one of the criteria defined below: * Incurable disease as assessed by surgical or radiation oncology * Metastatic (M1) disease * Persistent or progressive disease following curative-intent radiation, and not a candidate for surgical salvage due to incurability or morbidity. Patients who decline radical surgery are eligible. * In the dose-finding phase, patients may be cetuximab-exposed or cetuximab-naïve. If the most recent line of therapy included cetuximab, a two-week washout period without cetuximab dosing is required. * Patients must have previously received, not tolerated, or been judged clinically unsuitable for platinum-containing therapy. * In the dose-expansion phase, patients must be cetuximab-resistant by fulfilling at least one of the criteria defined below: * Disease recurrence within 6 months of completing definitive radiotherapy for locally advanced disease. Radiation must have included concurrent cetuximab. Induction chemotherapy, if given, may or may not have included cetuximab. * Disease progression during, or within 6 months, of cetuximab treatment in the recurrent/metastatic setting. Prior cetuximab exposure may have occurred in first, second and/or third line. * If the most recent line of therapy included cetuximab, a two-week washout period without cetuximab dosing is required. * Eastern Cooperative Oncology Group Performance Status 0-1 at time of informed consent (see Appendix B) * Age ≥ 18 years * Patients must consent to a research biopsy of tumor tissue at baseline, for conduct of correlative studies. Archived biopsy material may not be substituted. * Measurable disease per RECIST criteria, version 1.1 (see section 6) * Patients must have the following laboratory values measured within 28 days of registration: * Absolute neutrophil count (ANC) ≥ 1500/mm3 * Platelet count (PLT) ≥ 100,000/mm3 * Creatinine clearance ≥ 40 ml/min as determined by 24-hour collection or estimated by the Cockraft-Gault formula:Calculated Creatinine Clearance = \[(140-age) X (actual body weight in kg) X (0.85 if female)\]/(72 X serum creatinine) * Serum bilirubin ≤ 1.5 times upper-limit of normal (ULN) * AST (aspartate aminotransferase) and ALT (alanine aminotransferase) ≤ 3 times ULN * No prior severe infusion reaction to cetuximab or a monoclonal antibody * Written informed consent must be obtained from all patients prior to beginning therapy. Patients should have the ability to understand and the willingness to sign a written informed consent document. * If a woman of childbearing potential, documentation of negative pregnancy within 14 days prior to first dose of ficlatuzumab. Sexually active women of childbearing potential must agree to use adequate contraceptive measures, while on study and for 30 days after the last dose of study drug. All fertile female subjects (and their partners) must agree to use a highly effective method of contraception. Effective birth control includes (a) intrauterine device (IUD) plus one barrier method; or (b) 2 barrier methods. Effective barrier methods are male or female condoms, diaphragms, and spermicides (creams or gels that contain a chemical to kill sperm). Exclusion Criteria: Patients meeting any of the following exclusion criteria are not to be enrolled in the study: * Nasopharyngeal primary site, if WHO Type II or III (non-keratinizing) * History of severe allergic or anaphylactic reactions or hypersensitivity to recombinant proteins or excipients in the investigational agent. * Prior treatment with an HGF/cMet inhibitor such as rilotumumab, crizotinib, MetMAb, or ARQ197 * Uncontrolled central nervous system (CNS) metastases, including leptomeningeal metastases, are not allowed. Subjects with previously treated brain metastases will be allowed if the brain metastases have been stable without steroid treatment for at least 4 weeks following prior treatment (radiotherapy or surgery). * Failure to recover to Grade 1 or baseline from all toxic effects of previous chemotherapy, radiation therapy, biologic therapy, and/or experimental therapy, with the exception of: alopecia, Grade ≤ 2 peripheral neuropathy, Grade ≤ 2 cetuximab-related rash or other skin changes, hypomagnesemia (acceptable values detailed below), hypokalemia (acceptable values detailed below), and the acceptable hematologic values summarized above. A washout period of 2 weeks from prior cetuximab is required; a washout period of 3 weeks from any prior cytotoxic chemotherapy or investigational drug is required. * Significant pulmonary disease, including pulmonary hypertension or interstitial pneumonitis. * Decreased serum albumin \< 30 g/L (\< 3 g/dL) * Peripheral edema ≥ Grade 2 per NCI-CTCAE version 4.0. * Significant electrolyte imbalance prior to enrollment (note that patients may be supplemented to achieve acceptable electrolyte values): * Hypomagnesemia \<1.2 mg/dL or 0.5 mmol/L. * Hypocalcemia \< 8.0 mg/dL or 2.0 mmol/L. * Hypokalemia \< 3.0 mmol/L. * Significant dermatological disease including, but not limited to, skin drying and fissuring, paronychial inflammation, infectious sequelae (eg, blepharitis, cheilitis, cellulitis, cyst). Exception: patients with Grade ≤ 2 cetuximab-related rash, xerosis, fissures or paronychial inflammation are eligible. * Significant cardiovascular disease, including: * Cardiac failure New York Heart Association (NYHA) class III or IV. * Myocardial infarction, severe or unstable angina within 6 months prior to Study Day 1. * History of serious arrhythmia (i.e., ventricular tachycardia, or ventricular fibrillation). * Cardiac arrhythmias requiring anti-arrhythmic medications. * Significant thrombotic or embolic events within 4 weeks prior to Study Day 1. Significant thrombotic or embolic events include but are not limited to stroke or transient ischemic attack (TIA). Catheter-related thrombosis is not a cause for exclusion. Diagnosis of deep vein thrombosis or pulmonary embolism is allowed if it occurred \> 4 weeks prior to Study Day 1 and the patient is asymptomatic and stable on anti-coagulation therapy. * Any other medical condition (eg, alcohol abuse) or psychiatric condition that, in the opinion of the Investigator, might interfere with the subject's participation in the trial or interfere with the interpretation of trial results. * History of second malignancy within 2 years prior to Study Day 1 (except for excised and cured non-melanoma skin cancer, carcinoma in situ of breast or cervix, superficial bladder cancer, resected Stage I differentiated thyroid cancer, or T1a or T1b prostate cancer comprising \< 5% of resected tissue with normal prostate specific antigen (PSA) since resection). * Major surgery within 6 weeks prior to Study Day 1 (subjects must have completely recovered from any previous surgery prior to Study Day 1). * Active infection requiring antibiotics or antifungals within 7 days prior to first dose of study drug. * HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible drug interactions with study drugs. Appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated. Note: HIV testing is not required for entry into this protocol. * Women must not be pregnant or breastfeeding because ficlatuzumab and/or cetuximab may be harmful to the fetus or the nursing infant. Pregnant women are excluded from this study because ficlatuzumab and/or cetuximab have the potential for teratogenic or abortifacient effects.