Mitomycin C in Patients With Incurable p16 Positive Oropharyngeal and p16 Negative Head and Neck Squamous Cell Carcinoma (HNSCC) Resistant to Standard Therapies

Inclusion Criteria: * Histologically or cytologically confirmed incurable HNSCC of the oral cavity, oropharynx, larynx, hypopharynx, and/or Level 1-3 neck node with non-cutaneous SCC and unknown primary. "Incurable" is defined as metastatic disease or a local or regional recurrence in a previously irradiated site that is unresectable (or patient declines resection). * Progression following platin and immunotherapy given for incurable disease. * Measurable disease defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 10 mm with CT scan, as ≥ 20 mm by chest x-ray, or ≥ 10 mm with calipers by clinical exam per RECIST 1.1. * Tissue available (either initial diagnostic or recurrent tissue specimen) for p16 testing. * At least 18 years of age. * ECOG performance status ≤ 3 * Adequate hematologic, renal, and hepatic function as defined below: * Absolute neutrophil count ≥ 1,000/mcl * Platelets ≥ 75,000/mcl * Total bilirubin ≤ 1.5 mg/dL * AST(SGOT)/ALT(SGPT) ≤ 2.5 x ULN, alkaline phosphatase ≤ 2.5 x ULN, unless bone metastasis is present in the absence of liver metastasis * Creatinine below ULN (males 0.7-1.30 mg/dl; females 0.6-1.10 mg/dl) OR Creatinine clearance ≥ 60 mL/min/1.73 m2 for patients with creatinine levels above institutional normal * Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry, for the duration of study participation, and for 1 month after completing treatment. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). Exclusion Criteria: * Other active malignancy with the exception of basal cell or squamous cell carcinoma of the skin which were treated with local resection only, carcinoma in situ of the cervix, or synchronous H\&N primaries. * Currently receiving any other investigational agents. * 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 and/or breastfeeding. Patient must have a negative pregnancy test within 7 days of start of study treatment. * Known active central nervous system (CNS) metastases. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 28 days prior to treatment. * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to mitomycin C or other agents used in the study. * Known HIV-positivity on combination antiretroviral therapy because of the potential for pharmacokinetic interactions with the study drugs. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated.