Study of PX-866 and Docetaxel in Solid Tumors

Inclusion Criteria: * At least 18 years at time of consent * Agrees to use a medically accepted form of contraception from the time of consent to completion of all follow up study visits * If female of child bearing potential, negative pregnancy test (not required for post menopausal females) * Signed an informed consent document that has been approved by an institutional review board or independent ethics committee (IRB/IEC) * Has either locally advanced, recurrent, or metastatic NSCLC for which they have received at least 1 and no more than 2 prior systemic treatment regimens that may include up to 1 platinum based chemotherapy regimen and/or an epidermal growth factor receptor (EGFR) inhibitor OR locally advanced, recurrent or metastatic SCCHN for which they have received at least one and no more than two prior systemic treatment regimens. * Measurable disease per Response Evaluation Criteria In Solid Tumors * Eastern Cooperative Oncology Group (ECOG) 0 or 1 * In the opinion of the clinical investigator, life expectancy \>3 months * Adequate hematologic function as defined by: * Hemoglobin ≥ 9 g/dL * Absolute neutrophil count (ANC) ≥1500 cells/µL * Platelets ≥100,000/µL * Adequate hepatic function as defined by the following: * Bilirubin ≤ ULN * Aspartate aminotransaminase (AST/SGOT) and alanine aminotransferase (ALT/SGPT) ≤1.5 x upper limit of normal (ULN) * Creatinine level ≤1.5 x ULN Exclusion Criteria: * Has medical, social, or psychosocial factors that, in the opinion of the investigator, could impact safety or compliance with study procedures * Is breastfeeding * Treatment with any systemic chemotherapy, epidermal growth factor receptor (EGFR) inhibitor, radiation or experimental agent within 4 weeks of study drug dosing. Washout period following palliative radiation should be discussed with the study medical monitor * Previous treatment with docetaxel except for patients in Phase 2 who received a docetaxel containing regimen as part of adjuvant or neoadjuvant therapy which was completed at least 6 months prior to study drug dosing * Previous treatment with a phosphatidylinositol 3 kinase (PI 3K) inhibitor * Known human immunodeficiency virus (HIV) * Known or suspected clinically active brain metastases. Previously treated and stable brain metastases are allowable. Stable brain metastases are defined as no change on CT scan or MRI for minimum of two months AND no change in steroid dose for a minimum of four weeks, unless change due to intercurrent infection or other acute event * Grade \>2 peripheral neuropathy, as defined by the National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE), Version 4.02 * Any other significant medical or psychiatric condition that in the opinion of the investigator renders the patient inadequate for participation * History of severe hypersensitivity reactions to docetaxel or to other drugs formulated with polysorbate