Sorafenib, Docetaxel, and Cisplatin in Treating Patients With Metastatic or Advanced Gastric or Gastroesophageal Junction Cancer

Inclusion Criteria:

* Patients must have measurable, histologically confirmed, advanced unresectable or metastatic gastric or GEJ adenocarcinoma; imaging studies must be conducted within 4 weeks of study entry
* For patients with GEJ adenocarcinoma, the tumor location should be specified using the Siewert classification used in other NCI-sponsored Phase II studies in these disease sites
* Patients must have an ECOG performance status of 0-1
* Patients may have had adjuvant chemotherapy or chemoradiation therapy, with or without 5-Fluorouracil if the treatment was performed more than 6 months before any evidence of recurrent or metastatic disease
* Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately
* Must have the following baseline laboratory values obtained within 2 weeks of registration:

  * Absolute Granulocyte Count \>= 1,500/mm\^3
  * Platelet Count \>= 100,000/mm\^3
  * White Blood Count \>= 3,000/mm\^3
  * Serum Creatinine \<= 1.5 mg/dl
  * Total Bilirubin \<= 2.0 mg/dl
  * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT)/alkaline phosphatase (Alk phos) \<= 2.5 x upper limit of normal
* Patients must be able to take oral medication without crushing, dissolving or chewing tablets

Exclusion Criteria:

* Prior radiotherapy, chemotherapy or investigational therapies, particularly inhibitors of tyrosine Kinases, signal transduction or angiogenesis in the treatment for their recurrent and/or metastatic gastric or GEJ adenocarcinoma
* Receiving any other investigational agents
* Being pregnant or breast-feeding; all females of childbearing potential must have a blood or urine test within 2 weeks prior to registration to rule out pregnancy
* HIV-positive patients receiving combination antiretroviral therapy are excluded from the study because of possible pharmacokinetic interactions with BAY 43-9006
* Brain metastases
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to BAY 43-9006
* Acute active infection with significant clinical intervention per physician's discretion
* Previous or concurrent malignancies are not allowed, except:

  * Non-melanoma skin cancer and in situ cervical cancer
  * Treated cancer from which the patient has been continuously disease-free for more than five years
* Other uncontrolled intercurrent illnesses including, but not limited to: uncontrolled hypertension, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia or psychiatric illness/addictive disorders that would limit compliance with study requirements
* Evidence of bleeding diathesis
* Concurrent cytochrome P450 enzyme-inducing anti-epileptic drugs:

  * Phenytoin
  * Carbamazepine
  * Phenobarbital
  * Rifampin
  * St. John's Wort