Study of Modified Docetaxel, Cisplatin, and Fluorouracil (mDCF) in Unresectable or Metastatic Gastric and Gastroesophageal Junction Adenocarcinoma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed metastatic or unresectable gastric or gastroesophageal junction (GEJ) adenocarcinoma. GEJ adenocarcinoma may be classified according to Siewert's classification type I, II, or III\[43\]. * Histological documentation of local recurrence or metastasis is strongly encouraged, unless the risk of such a procedure outweighs the potential benefit of confirming the metastatic disease. * If no histologic confirmation, then the metastases or recurrence will require documentation by a 2nd radiographic procedure (eg. PET/CT scan or MRI in addition to the CT scan). If the imaging procedure does not confirm recurrent or metastatic disease, biopsy confirmation will be required. * Patients must have disease that can be evaluated radiographically. This may be measurable disease or non-measurable disease. Measurable disease is defined as that which can be measured in at least one dimension as \> 20 mm with conventional techniques, or \>10 mm by high resolution imaging. Disease that is identified on radiology studies, but does not meet the criteria for measurable disease, is considered non-measurable. * Patients may have received no prior chemotherapy for metastatic or unresectable disease. Patients may have received prior adjuvant therapy (chemotherapy and/or chemoradiation) if more than 6 months have elapsed between the end of adjuvant therapy and registration. Patients may not have received prior docetaxel or cisplatin. * Age 18 years or older. * Karnofsky performance status \> than or = to 70% (ECOG performance status 0-1). * Peripheral neuropathy \< than or = to grade 1. * Hematologic (minimal values): * White blood cell count \> than or = to 3000/mm3 * Absolute neutrophil count \> than or = to 1500 cells/ mm3 * Hemoglobin \> than or = to 9.0 g/dl * Platelet count \> than or = to 100,000 / mm3 * Hepatic (minimal values): * Total bilirubin \< or = to 1.5 \* \* AST and ALT and Alkaline phosphatase must be within the eligible range. In determining eligibility, the more abnormal of the two values (AST or ALT) should be used. Patients with alkaline phosphatase elevation secondary to the bony metastases rather than liver dysfunction may proceed with treatment on protocol after discussion with the principal investigator. * Kidney function (minimal values): \* Serum creatinine \< than or = to 1.5 mg/dl - if serum creatinine is 1.2-1.5 mg/dl, the creatinine clearance (either measured or calculated) must be 50 ml/min or greater * The patient has a PT (INR) \< than or = to 1.5 and an PTT \< than or = to 3 seconds above the upper limits of normal if the patient is not on anticoagulation. If a patient is on full-dose anticoagulants, the following criteria should be met for enrollment: * The patient must have an in-range INR (usually between 2 and 3) on a stable dose of warfarin or on stable dose of LMW heparin * The patient must not have active bleeding or pathological conditions that carry high risk of bleeding (e.g. tumor involving major vessels, known varices) * Women of childbearing potential have a negative pregnancy test. * Men and women of childbearing potential must be willing to consent to using effective contraception while on treatment and for at least 3 months thereafter. * Ability to understand informed consent and signing of written informed consent document prior to initiation of protocol therapy. * Patients must have HER2-positive (FISH+ or IHC 3+) metastatic or unresectable gastric or gastroesophageal junction (GEJ) adenocarcinoma to be eligible for trastuzumab. For the purposes of this protocol, FISH+ is defined as HER2:CEP17 ratio ≥ 2.0. Biopsy samples with cohesive IHC3+ or FISH+ clones are considered HER2 positive irrespective of size, i.e.\<10%. FISH+ defined as \>2 HER2:CEP17. * Patients who are receiving trastuzumab must have a left ventricular ejection fraction of ≥ 50%. Exclusion Criteria: * Patients who have received previous chemotherapy for the treatment of metastatic or unresectable gastric or GEJ adenocarcinoma are ineligible. * Patients who have received previous pre- or post-operative chemotherapy or chemoradiation are ineligible if therapy was completed less than 6 months prior to study registration. Patients must have recovered from adverse events from any previous therapy. * Patients who have received previous docetaxel or cisplatin. * Patients with a history of another neoplastic disease within the past three years, excluding basal cell carcinoma of the skin, cervical carcinoma in situ, or nonmetastatic prostate cancer. * Patients with brain or central nervous system metastases, including leptomeningeal disease. * Pregnant (positive pregnancy test) or breast feeding. * Serious, non-healing wound, ulcer, or bone fracture. * Significant cardiac disease as defined as: unstable angina, New York Heart Association (NYHA) grade II or greater, congestive heart failure, history of myocardial infarction within 6 months * Evidence of bleeding diathesis or coagulopathy. * History of a stroke or CVA within 6 months * Clinically significant peripheral vascular disease. * Clinically significant hearing loss or ringing in the ears. * Patients with a history of severe hypersensitivity reaction to Taxotere® or other drugs formulated with polysorbate 80. * Inability to comply with study and/or follow-up procedures. * Patients with any other medical condition or reason, in that investigator's opinion, makes the patient unstable to participate in a clinical trial. * For patients who are Her2 positive and will be treated on the trastuzumab + mDCF cohort, prior trastuzumab treatment is not allowed. * For patients who are Her2 positive and will be treated on the trastuzumab+mDCF cohort, left ventricular function \<50%