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 t…