Inclusion Criteria:

- Histologically/cytologically confirmed diagnosis of squamous cell carcinoma of head
and neck origin not amenable to curative intent therapy; both human papillomavirus
(HPV) positive (+) and HPV negative (-) are eligible, but status has to be known
prior to randomization; any type of tissue based HPV assessment is acceptable (e.g.
p16 immunohistochemistry [IHC] or in situ hybridization [ISH]); if local HPV testing
is not available slides can be sent to the University of Chicago for HPV testing
using p16 IHC or comparable

- Presence of measurable lesions (Response Evaluation Criteria in Solid Tumors
[RECIST])

- Availability of tissue (>= 17 tumor containing formalin-fixed, paraffin-embedded
[FFPE] slides/sections)

- Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1

- Patients who have received cetuximab or another inhibitor of epidermal growth factor
receptor (EGFR) in the curative intent treatment setting (e.g. with radiation or
during induction chemotherapy [prior to definitive, curative intent therapy]) are
eligible for the study

- Life expectancy of greater than 8 weeks

- Hemoglobin >= 9.0 g/dL

- Leukocytes >= 3,000/mcL

- Absolute neutrophil count >= 1,500/mcL

- Platelets >=100,000/mcL

- Total bilirubin =< 1.5 X institutional upper limit of normal

- Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
[SGOT])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase [SGPT])
=< 2.5 X institutional upper limit of normal

- Serum creatinine =< 1.5 X institutional upper limit of normal OR creatinine clearance
>= 60 mL/min/1.73 m^2 for patients with creatinine levels above institutional normal

- Presence of measurable lesions by RECIST: 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) as >= 20 mm with conventional techniques
or as >= 10 mm with spiral computed tomography (CT) scan

- Human immunodeficiency virus (HIV)-positive patients with normal immune function
(cluster of differentiation [CD]4 count > 200) are eligible if there are no drug
interactions with ARQ 197 (tivantinib) or cetuximab

- Women of child-bearing potential and men must agree to use adequate contraception
(hormonal or barrier method of birth control; abstinence) prior to study entry and
for the duration of study participation; should a woman become pregnant or suspect
she is pregnant while she or her partner is participating in this study, she should
inform her treating physician immediately; men treated or enrolled on this protocol
must also agree to use adequate contraception prior to the study, for the duration of
study participation, and 4 months after completion of ARQ 197 (tivantinib)
administration

- Ability to understand and the willingness to sign a written informed consent document

- Patients must be able to swallow ARQ 197 (tivantinib) by mouth, unless adequate data
about administration by gastronomy tube (G-tube) becomes available

Exclusion Criteria:

- Patients who have ad chemotherapy or radiotherapy within 2 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 2 weeks earlier

- Patients with tumors that progress within 3 months of definitive treatment (typically
chemoradiation or radiation) are ineligible

- Patients who have received more than 2 prior cytotoxic treatments in the palliative
treatment setting are ineligible

- Patients who have received treatment with an EGFR or MET inhibitor in the palliative
treatment setting are ineligible

- Patients with known, active brain metastases should be excluded from this clinical
trial; patients with treated brain metastases stable for >= 12 weeks are eligible;
use of corticosteroids is acceptable on a low maintenance or tapering dose schedule

- History of allergic reactions attributed to compounds of similar chemical or biologic
composition to ARQ 197 (tivantinib) or cetuximab

- Concurrent life-threatening diseases: patients with diseases which with reasonable
certainty do not limit life expectancy to 12 months or less are eligible; assessment
of such concurrent illnesses should be by the principal investigator

- 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; breastfeeding should be discontinued if
the mother is treated with ARQ 197 (tivantinib)

- Concurrent use of warfarin (therapeutic use) is allowed, but requires close
monitoring of prothrombin time (PT)/international normalized ratio (INR)

- ARQ 197 (tivantinib) is metabolized by cytochrome P450 2C19 (CYP2C19), and to a
lesser extent cytochrome P450 3A4 (CYP3A4); the metabolism and consequently overall
pharmacokinetics of ARQ 197 (tivantinib) could be altered by inhibitors and/or
inducers or other substrates of CYP2C19 and CYP3A4; while inhibitors/inducers of
these cytochrome P450 isoenzymes are not specifically excluded, investigators should
be aware that ARQ 197 (tivantinib) exposure may be altered by the concomitant
administration of these drugs

- History of congestive heart failure defined as class II to IV per New York Heart
Association (NYHA) classification; clinically significant bradycardia or other
uncontrolled, cardiac arrhythmia defined as >= grade 3 according to National Cancer
Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), version 4.0,
or uncontrolled hypertension; myocardial infarction occurring within 6 months prior
to study entry (myocardial infarction occurring > 6 months prior to study entry is
permitted)

- Patients may not be receiving any other investigational agents