This phase II trial studies how well combination chemotherapy works in treating patients with advanced stomach, gastroesophageal, or esophageal cancer. Drugs used in chemotherapy, such as irinotecan hydrochloride, oxaliplatin, leucovorin calcium, and fluorouracil, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving more than one drug (combination chemotherapy) may kill more tumor cells.

Inclusion Criteria:

1. Biopsy-proven and inoperable locally advanced, recurrent, or metastatic cancer of the esophagus, stomach, or gastro-esophageal junction.

2. Measurable disease defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥10 mm with CT scan, as ≥20 mm by chest x-ray, or ≥10 mm with calipers by clinical exam.

3. Prior single modality radiation therapy is allowed.

4. At least 18 years of age.

5. ECOG performance status ≤ 2

6. Normal bone marrow and organ function as defined below:

   1. Absolute neutrophil count ≥ 1,500/mcl
   2. Platelets ≥ 100,000/mcl
   3. AST(SGOT)/ALT(SGPT) ≤ 2.5 x IULN
   4. Creatinine ≤ IULN OR creatinine clearance ≥ 60 mL/min/1.73 m2 for patients with creatinine levels above institutional normal
   5. LVEF ≥ 50%

7. Women of childbearing 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 must inform her treating physician immediately.

8. Ability to understand and willingness to sign an IRB approved written informed consent document (legally authorized representative is allowed).

9. Patients already receiving treatment with FOLFIRINOX +/- trastuzumab may participate in the study and have their data collected retrospectively if they met inclusion criteria at the start of therapy and sign consent for study participation moving forward.

Exclusion Criteria:

1. Chemotherapy in the 6 months prior to registration.
2. Any active malignancy within 3 years that may alter the course of esophageal cancer (Apparently cured localized malignancy or advanced, but indolent malignancy with significantly more favorable prognosis are allowed)
3. Receiving any other investigational agents at the time of registration.
4. Known untreated brain metastases. These patients must be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events.
5. A history of allergic reactions attributed to compounds of similar chemical or biologic composition to the agents used in the study.
6. Previous therapy for metastatic gastroesophageal cancer. Previous perioperative chemotherapy is allowed as long as the duration without treatment has been greater than 6 months..
7. A history of congestive heart failure, transmural myocardial infarction, symptomatic valvular disease, or high-risk arrhythmia.
8. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
9. Pregnant and/or breastfeeding. Patient must have a negative urine pregnancy test within 14 days of study entry.
10. Known HIV-positivity and on combination antiretroviral therapy because of the potential for pharmacokinetic interactions with trastuzumab. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated.

Inclusion of Women and Minorities

Both men and women and members of all races and ethnic groups are eligible for this trial.