This phase II trial studies how well pralatrexate and oxaliplatin work in treating patients with esophageal, stomach, or gastroesophageal junction cancer that cannot be removed by surgery or has spread from the primary site (place where it started) to other places in the body. Pralatrexate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as oxaliplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving pralatrexate with oxaliplatin may be an effective treatment for esophageal, stomach, or gastroesophageal junction cancer.

PRIMARY OBJECTIVES:

I. To determine the overall response rate in patients with advanced esophago-gastric cancer (EGC) to combination pralatrexate and oxaliplatin.

SECONDARY OBJECTIVES:

I. To examine the toxicity and tolerability of this regimen. II. To determine the time-to-progression and overall survival using this regimen.

III. To examine whether functionally relevant polymorphisms of genes of the folate metabolism pathway correlate with efficacy and toxicity of pralatrexate.

IV. To examine whether response to pralatrexate can be predicted by micro-ribonucleic acid (microRNA) expression profiling of the epithelial component of the tumor.

OUTLINE:

Patients receive pralatrexate intravenously (IV) over 3-5 minutes and oxaliplatin IV over 2 hours on day 1. Courses repeat every 2 weeks in the absence of disease progression or unacceptable toxicity. Oxaliplatin will be discontinued after 12 courses.

After completion of study treatment, patients are followed up for 30 days and then periodically thereafter for up to 5 years.

Inclusion Criteria:

• Histologically confirmed carcinoma of the esophagus, stomach or gastro-esophageal junction that is metastatic, or locally advanced and inoperable for cure; histological sub-types permitted include adenocarcinoma, squamous-cell carcinoma, or undifferentiated carcinoma; small-cell carcinoma variant is not eligible
• No previous systemic therapy for metastatic or recurrent disease; therapy (chemotherapy, radiotherapy, or both) administered in the neo-adjuvant, adjuvant, or definitive setting for previously localized disease is permitted, provided it was completed more than 6 months prior to enrollment; palliative radiotherapy is permitted provided it is completed >= 3 weeks prior to study therapy initiation
• Eastern Cooperative Oncology Group (ECOG) performance status 0-2
• Life expectancy >= 12 weeks
• Hemoglobin >= 9 g/dl
• Absolute neutrophil count >= 1500/mm^3
• Platelet count >= 100,000/mm^3
• Serum creatinine =< institutional upper limit normal (ULN)
• Bilirubin =< 1.5 x ULN
• Transaminases =< 3 x ULN; for documented liver metastases, transaminases up to 5 x ULN is permitted
• No evidence of >= grade 2 peripheral neuropathy
• Patients with reproductive potential must be willing to use an adequate contraceptive method (e.g., abstinence, intrauterine device, oral contraceptives, barrier device with spermicide or surgical sterilization) during treatment and for three months after completing treatment; a negative pregnancy test is required for women of child-bearing potential; nursing women are ineligible
• Written, informed consent

Exclusion Criteria:

• Hypersensitivity to platinum compounds
• Uncontrolled inter-current illness including but not limited to active infection, symptomatic congestive heart failure, unstable angina, uncontrolled cardiac arrhythmia, or psychiatric illness that would limit compliance with study requirements
• Presence of brain metastases
• Patients with third-space (pleural, peritoneal) fluid not controllable with usual drainage methods are not eligible
• History of second primary malignancy within 3 years prior to enrollment, except for in-situ cervix carcinoma or non-melanoma skin cancer
• Undergone an allogeneic stem cell transplant