Inclusion Criteria:

1. Histologically confirmed SCC; only patients with HNSCC, non-small cell lung SCC, skin
SCC, cervical SCC, penile SCC, anal SCC, and esophageal SCC;

2. For patients with HNSCC only, HPV status assessed by in situ hybridization (ISH)
and/or p16 immunohistochemistry (IHC) according to local standards;

3. Incurable, non-resectable local relapsed and/or distant metastatic disease after no
more than 3 prior treatment regimens for advanced cancer, one of which must be
platinum-based chemotherapy or chemo-radiation therapy;

4. Eastern Cooperative Oncology Group (ECOG) performance status ≤2;

5. Life expectancy of at least 3 months;

6. Measurable disease according to RECIST version 1.1;

7. Ability to swallow entire capsules;

8. Adequate hematologic function;

9. Adequate hepatic function;

10. Adequate renal function

11. Adequate contraceptive regimens for female and male patients.

12. Female patients with reproductive potential must have a negative urine or serum
pregnancy test;

13. Ability to understand the nature of the study and any hazards of study participation,
to communicate satisfactorily with the Investigator, and to follow the requirements
of the entire protocol;

14. Willingness to adhere to the prohibitions and restrictions specified in this
protocol;

15. The patient must sign an informed consent form (ICF).

Exclusion Criteria:

1. Chemotherapy or any potentially myelosuppressive treatment within 3 weeks prior to
enrollment (6 weeks are required for nitrosoureas or mitomycin C);

2. Prior doxorubicin therapy at a total cumulative dose exceeding 450 mg/m2;

3. Definitive radiotherapy (ie, over 10 fractions and maximal area of hematopoietic
active bone marrow treated ˃25%) within 4 weeks prior to enrollment;

4. Palliative radiotherapy (ie, 10 fractions or less) within 2 weeks prior to
enrollment;

5. Systemic administration of corticosteroids within the past 4 weeks prior to
enrollment;

6. Prior therapy with a phosphatidylinositol 3-kinase (PI3K), Akt or mammalian target of
rapamycin (mTOR) inhibitor;

7. Any other investigational agent or chemotherapy, radiotherapy, or immunotherapy
within 4 weeks of enrollment;

8. Major surgery within 3 weeks of enrollment or major surgery without full recovery;

9. Residual clinical signs and symptoms which have not recovered to Common Terminology
Criteria for Adverse Events (CTCAE) version 4 Grade 1 severity level or below before
enrollment, except for alopecia, stable residual neuropathy, and residual hand/foot
syndrome;

10. Known brain metastases, except for those that have been removed or irradiated and
have no current clinical impact at the time of enrollment; a computed tomography (CT)
scan or magnetic resonance imaging (MRI) of the brain should be obtained in patients
with symptoms suggestive of brain metastases;

11. Ascites requiring active medical management, including paracentesis;

12. Serum sodium less than 130 mEq/L or conditions that may predispose patients to
hyponatremia (eg, previous syndrome of inappropriate antidiuretic hormone
hypersecretion [SIADH], chronic diuretic use, etc.);

13. Uncontrolled intercurrent illness including, but not limited to, ongoing or active
infection, bleeding, symptomatic congestive heart failure, unstable angina pectoris,
and cardiac arrhythmia;

14. Uncontrolled hypertension, defined as systolic blood pressure ≥160 mmHg and/or
diastolic blood pressure ≥110 mmHg;

15. New onset of seizures within 3 months prior to enrollment, or poorly controlled
seizures;

16. Psychiatric illness/social situations that would limit the patient's ability to
tolerate and/or comply with study requirements;

17. History of allergic reactions attributed to compounds of similar chemical or biologic
composition to rigosertib;

18. Female patients who are pregnant or lactating.