Oral Rigosertib for Squamous Cell Carcinoma

This will be a multicenter, Phase II study to evaluate the safety and efficacy of oral rigosertib in patients with relapsed or metastatic squamous cell carinoma (SCC) who previously received platinum-based chemotherapy and/or chemo-radiation therapy. Only patients with head and neck squamous cell carinoma (HNSCC), non-small cell lung SCC, skin SCC, cervical SCC, penile SCC, anal SCC or esophageal SCC will be enrolled in the study. Patients will be administered rigosertib capsules at a dose of 560 mg BID on days 1 to 14 of a 21-day cycle. Patients will be enrolled in 2 cohorts based on HPV test results: * Cohort 1 will include up to 40 patients with human papillomavirus (HPV)-positive SCC, of which approximately 30 patients will have HNSCC, and approximately 10 patients with SCC of another origin (eg, cervix, anal, penile); * Cohort 2 will include up to 40 patients with HPV-negative SCC, of which approximately 30 patients will have HNSCC, and approximately 10 patients with SCC of another origin (eg, lung, skin, esophageal). Patients will be evaluated for progression after completing 3 cycles of therapy and every 3 cycles thereafter. Patients with stable disease (SD) or better, based on revised Response Criteria in Solid Tumors (mRECIST) 1.1, will receive repeated cycles of treatment on a 21-day cycle schedule until disease progression, development of unacceptable toxicity, or withdrawal of consent. Patients with progressive disease (PD) but who, in the opinion of the Investigator, appear to be deriving clinical benefit, may continue on study with a planned disease reassessment after one further cycle of therapy. Should the patient have SD or PR at this reassessment, s/he may continue on study, with subsequent reassessments every 3 cycles. Following discontinuation of rigosertib treatment, patients' mortality status will be assessed every 3 months.