Brief Summary: This study is being done to determine the dose of a chemotherapy drug (irinotecan \[irinotecan hydrochloride\]) that can be tolerated as part of a combination of drugs. There is a combination of chemotherapy drugs often used to treat gastrointestinal cancer, which consists of 5-FU (fluorouracil), leucovorin (leucovorin calcium), irinotecan and oxaliplatin and is known as "FOLFIRINOX". FOLFIRINOX is a current drug therapy combination (or regimen) used for people with advanced pancreatic cancer, although this combination is not Food and Drug Administration (FDA) approved for this indication. FOLFIRINOX was recently shown in a separate clinical trial to increase survival compared to another commonly used drug in pancreatic cancer called gemcitabine. FOLFIRINOX is also a reasonable regimen for those with other advanced cancers of the gastrointestinal tract, including colon cancer, rectal cancer, esophagus cancer, stomach cancer, gall bladder cancer, bile duct cancer, ampullary cancer, and cancers with an unknown primary location. The best dose of irinotecan to use in FOLFIRINOX is not known. This study will analyze one gene (uridine 5'-diphospho \[UDP\] glucuronosyltransferase 1 family, polypeptide A1 \[UGT1A1\] gene) of subjects for the presence of an alteration in that gene, which may affect how the body handles irinotecan. Genes help determine some of the investigators individual characteristics, such as eye color, height and skin tone. Genes may also determine why people get certain diseases and how medicines may affect them. The result of the genetic analysis will divide subjects into one of three groups: A, B, or C. Group A (approximately 45% of subjects) will receive the standard dose of irinotecan. Group B (approximately 45% of subjects) will receive a lower dose of irinotecan. Group C (approximately 10% of subjects) will receive an even lower dose of irinotecan

Detailed Description: PRIMARY OBJECTIVES: I. To determine the dose-limiting toxicity (DLT) rate in cycle #1 in each of two UGT1A1 genotype groups (\*1\*1, \*1\*28) using genotype-guided dosing of irinotecan as part of the modified (m) FOLFIRINOX regimen. SECONDARY OBJECTIVES: I. To determine the cumulative dose intensity of irinotecan achieved in each genotype group. II. To determine the response rates by Response Evaluation Criteria in Solid Tumors (RECIST) (version 1.1) for each different disease (pancreatic cancer, biliary cancers, gastric cancer, colorectal cancer, adenocarcinoma of unknown primary) treated in the study. OUTLINE: Patients receive oxaliplatin intravenously (IV) over 2 hours, irinotecan hydrochloride IV over 1.5 hours, leucovorin calcium IV over 2 hours, and fluorouracil IV continuously over 46 hours on days 1 and 15. Treatment repeats every 4 weeks for up to 6 courses in the absence of disease progression or unacceptable toxicity.