Treatment of cancer is often improved if two or more drugs are used in combination. In animal studies, the use of the combination of ON 01910.Na (a new, unapproved drug) and irinotecan or oxaliplatin (two approved and extensively used anti-cancer drugs) gave better results against tumor cells than the use of any of the single drugs alone. In addition, the use of the combinations did not result in an increase of side effects. This clinical trial will determine what is the highest dose of ON 01910.Na that can be given safely in combination with either irinotecan or oxaliplatin in human patients.

This is an open-label, 2-arm, dose-escalation combination-therapy study in which patients with advanced malignancies will be assigned by the Investigator to dosing with either irinotecan plus ON 01910.Na (Group A), or oxaliplatin plus ON 01910.Na (Group B). The Investigator will make this assignment using clinical judgment, taking into consideration the patient's tumor type, UGT1A1 genotype when applicable (i.e., patients considered for treatment in Group A will be tested for UGT1A1 genotype, if not already known, and patients homozygous for the UGT1A1*28 allele will be excluded from Group A), prior treatment, and current clinical condition. Patients will be enrolled in 1 of 8 Cohorts (4 sequential Cohorts in Group A and 4 in Group B) of 3 patients each. Up to 6 additional patients will be tested at the MTD. Groups A and B will enroll and proceed simultaneously.

Inclusion Criteria:

• Male and female patients ≥18 years of age with histologically or cytologically confirmed solid tumors that are metastatic or progressive, for whom no standard therapy holds curative potential and for whom irinotecan or oxaliplatin are reasonable treatment options.
• Patients must have evaluable disease, either measurable on imaging or with informative tumor marker(s).
• Eastern Collaborative Oncology Group (ECOG) Performance Status of ≤2.
• Life expectancy >12 weeks.
• Any acute or chronic adverse effects of prior chemotherapy have resolved to <Grade 2 as determined by CTCAE v3 criteria.
• Existing or planned central venous access with a 2-channel infusion catheter system.
• Laboratory values meet the following criteria: Absolute neutrophil count ≥1,500 cells/µL; Platelets ≥100,000 cells/µL; Total bilirubin ≤1.5 times the upper limit of normal; AST (SGOT) ≤2.5 times the upper limit of normal; ALT (SGPT) ≤2.5 times the upper limit of normal; Serum creatinine ≤1.5 mg/dL or a measured creatinine clearance ≥50 mL/min; Negative βhCG test in women of childbearing potential (defined as women ≤50 years of age or history of amenorrhea for ≤12 months prior to study entry).
• Patients with primary liver cancer or hepatic metastasis are eligible to enroll, provided they meet the following: Total bilirubin is ≤2 mg/dL; AST and ALT are each ≤5 times the institutional upper limit of normal; Ascites, if present, is manageable with diuretic agents alone.
• If there is a history of treated brain metastases, these must have been clinically stable for ≥4 weeks prior to enrollment.
• UGT1A1 genotype of patient must be known or a UGT1A1 genotype test must be done for patients being considered for treatment in Group A.

Exclusion Criteria:

• Women who are pregnant or lactating.
• Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study.
• Severe liver dysfunction (Child-Pugh Class C or uncompensated Class B with persistent encephalopathy, persistent ascites, or prothrombin time >1.5 times the upper limit of normal) is present.
• Patients with a history of esophageal bleeding are excluded unless varices have been sclerosed or banded and bleeding episodes have not occurred during the prior 6 months.
• Contraindications, including known hypersensitivity, to the assigned chemotherapy agent (i.e., irinotecan or oxaliplatin).
• Prior receipt of ON 01910.Na or prior participation in this protocol.
• Use of any investigational agents within 4 weeks of study enrollment.
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements, as determined by the Investigator.
• Patients who are homozygous for the UGT1A1*28 allele will be excluded from participating in Group A of this protocol.
• Patients with ascites requiring active medical management including paracentesis, peripheral bilateral edema or hyponatremia (defined as serum sodium value of <134 Meq/L).