Ficlatuzumab w/wo Cetuximab in Patients w/Cetuximab-Resistant, Recurrent or Metastatic Head/Neck Squamous Cell Carcinoma

Inclusion Criteria: \- Patients must have histologically confirmed HNSCC from any primary site, except nasopharyngeal if World Health Organization (WHO) Type III (non-keratinizing and Epstein-Barr virus (EBV)-positive)). Eligible histologies include: * Basaloid, poorly differentiated, and undifferentiated carcinoma histologies. * Nasopharyngeal carcinoma, WHO Type I and II (keratinizing, non-EBV positive). * Paranasal sinus, lip and external auditory canal sites. * Squamous cell carcinoma of unknown primary, clearly related to the head and neck. Note: Documentation of primary site diagnosis must be submitted with the registration request. * Patients must have recurrent and/or 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. Note: Patients who decline radical surgery are eligible. * For patients with oropharyngeal primary site or unknown primary site only: Patients must have known tumoral HPV status (p16). (Acceptable standards include p16 immunohistochemistry (where a tumor is classified as p16-positive when showing diffuse nuclear and cytoplasmic staining in at least 70% of tumor cells) and/or assessment of HPV DNA.) Note: For these subjects, documentation of p16 status must be submitted with the registration packet. * Patients must be cetuximab-resistant by fulfilling at least one of the two criteria defined below: * Disease persistence or recurrence within 6 months of completing definitive radiotherapy with concurrent cetuximab for locally advanced disease. Induction chemotherapy, if given, may or may not have included cetuximab. * Disease progression during, or within 6 months, of cetuximab treatment in the recurrent and/or metastatic setting. Note: Prior cetuximab exposure may have occurred in any line of therapy (first line, second line, etc.) and is not required to be the most recent therapy received. * Patients must be platinum-resistant or platinum-ineligible by fulfilling at least one of the three criteria defined below: * Disease persistence or recurrence within 6 months of completing definitive radiotherapy for locally advanced disease, where platinum chemotherapy was administered as a component of induction and/or concurrent systemic treatment. * Disease progression during, or within 6 months, of treatment with platinum chemotherapy (e.g., carboplatin or cisplatin) in the recurrent and/or metastatic setting. * The patient is not an acceptable candidate for platinum chemotherapy due to medical comorbidities, in the judgment of the local investigator. Note: Prior platinum exposure may have occurred in any line of therapy (first line, second line, etc.) and is not required to be the most recent therapy received. \- Patients must have prior exposure to an anti-PD1 (programmed cell death protein 1) or anti-PDL1 (programmed cell death ligand 1) monoclonal antibody (mAb), if eligible for immunotherapy in the judgment of the local investigator. Note: Prior exposure to investigational immunotherapies, including anti-CTLA4 (cytotoxic T-lymphocyte-associated antigen 4), anti-OX40, anti-CD40 (cluster of differentiation 40), anti-CD27, anti-TNFR (tumor necrosis factor receptor) antibodies or other investigational immunotherapies, is acceptable. * Patients must have Eastern Cooperative Oncology Group (ECOG) Performance Status 0-1 at time of informed consent (see Appendix B). * Patients must be age ≥ 18 years. * Patients must consent to a research biopsy of tumor tissue at baseline, for conduct of correlative studies. In cases where a fresh biopsy is not feasible (i.e., if an accessible tumor site cannot be biopsied with acceptable clinical risk), archival tissue may be submitted instead, after discussion with and approval by the Sponsor-Investigator. * Patients must have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) criteria, version 1.1 (see section 6) per scan within 28 days prior to registration. * Patients must have adequate electrolytes, liver, renal, and hematology function as defined below within 28 days of registration: * Absolute neutrophil count (ANC) ≥ 1500/mm3 * Platelet count (PLT) ≥ 75,000/mm3 * Creatinine clearance ≥ 30 mL/min per 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) \* Total bilirubin ≤ 1.5 times upper-limit of normal (ULN) * AST (aspartate aminotransferase) ≤ 3 times ULN * ALT (alanine aminotransferase) ≤ 3 times ULN * Magnesium ≥ 1.2 mg/dL or 0.5 mmol/L * Corrected Calcium ≥ 8.0 mg/dL or 2.0 mmol/L * Potassium ≥ 3.0 mmol/L (Note: Patients may be supplemented to achieve acceptable electrolyte values.) * Serum albumin ≥ 25 g/L (≥ 2.5 g/dL) * Patients must sign written informed consent prior to beginning study screening procedures. Patients must have the ability to understand and the willingness to sign a written informed consent document. * Women of child-bearing potential (WOCBP) must agree to have a pregnancy test within 14 days prior to registration and a repeated test within 3 days of the first dose of ficlatuzumab. * Patients must agree to use highly effective contraceptive measures while on study and for 60 days after the last dose of study drug. This includes: Men of reproductive potential AND women of childbearing potential. * 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 * Nasopharyngeal primary site if WHO Type III (non-keratinizing and EBV-positive as established at the local site). * 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 tivantinib (ARQ197). * Uncontrolled central nervous system (CNS) metastases, including leptomeningeal metastases, are not allowed. Note: Subjects with previously treated brain metastases will be allowed if the brain metastases have been stable without steroid treatment for at least 2 weeks (radiotherapy or surgery). * Failure to recover to Grade 1 or baseline from all toxic effects of previous chemotherapy, radiation therapy, biologic therapy, immunotherapy, 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 in the exclusion criteria below), * Hypokalemia (acceptable values detailed in the exclusion criteria below), and * The acceptable ANC and PLT inclusion criteria values above. * Treatment with cetuximab 2 weeks prior to the first dose of study drug. A washout period of 2 weeks from prior cetuximab is required if applicable. * Treatment with cytotoxic chemotherapy, targeted therapy, immunotherapy or investigational drug 3 weeks prior to the first dose of study drug. A washout period of 3 weeks from any prior cytotoxic chemotherapy, targeted therapy, immunotherapy or investigational drug is required, if applicable. * Significant underlying pulmonary disease, including pulmonary hypertension or interstitial pneumonitis. * Peripheral edema ≥ Grade 2 per NCI-CTCAE version 4.0. * Significant cardiovascular disease, including: * Cardiac failure New York Heart Association (NYHA) class III or IV. * Myocardial infarction within 6 months prior to registration. * Severe or unstable angina within 6 months prior to registration. * History of serious ventricular arrhythmia (i.e., ventricular tachycardia or ventricular fibrillation). * Cardiac arrhythmia requiring anti-arrhythmic medication(s). (Beta-blockers, calcium channel blockers, and digoxin administered for the purpose of rate control of supraventricular tachycardia, including atrial fibrillation and atrial flutter, are not classified as anti-arrhythmic medications for purposes of trial eligibility.) * Significant thrombotic or embolic events within 28 days prior to registration. (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 \> 28 days prior to registration and the patient is asymptomatic and stable on anti-coagulation therapy.) * Any other medical condition (e.g., alcohol abuse) or psychiatric condition that, in the opinion of the local 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 registration except: * Excised and cured non-melanoma skin cancer, * Carcinoma in situ of breast or cervix, * Superficial bladder cancer, * Stage I differentiated thyroid cancer that is resected or observed, * pT1a /pT1b prostate cancer comprising \< 5% of resected tissue with normal prostate specific antigen (PSA) since resection, or \* cT1a/cT1b prostate cancer treated with brachytherapy or external beam radiation therapy with normal PSA since radiation. * Not completely recovered from any previous surgery. Note: Complete recovery is in the opinion of the treating investigator. Consult the Sponsor-Investigator, if needed. * Active systemic infection requiring systemic antibiotics or antifungals within 7 days prior to first dose of study drug, except tetracycline family antibiotics (tetracycline, doxycycline, minocycline) administered for the management of cetuximab-related rash may be continued per the Investigator's judgment. Note: Active topical infections (for example oral thrush) do not exclude a subject even if treated with systemic antibiotics or systemic antifungals. * History of severe infusion reaction to cetuximab or a monoclonal antibody. * Known to be Human immunodeficiency virus (HIV) positive. Note: HIV testing is not required for entry into this protocol. * Women who are pregnant or breastfeeding. (A negative urine pregnancy test must be confirmed within 14 days of registration and repeated within 3 days of the first dose of study drug.)