Pralatrexate and Docetaxel in Treating Patients With Stage IV Esophageal or Gastroesophageal Cancer Who Have Failed Platinum-Based Therapy

RATIONALE: Pralatrexate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as docetaxel, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving pralatrexate together with docetaxel may kill more tumor cells.

PURPOSE: This phase II trial is studying how well giving pralatrexate together with docetaxel works in treating patients with stage IV esophageal or gastroesophageal cancer who have failed platinum-based therapy.

PRIMARY OBJECTIVES:

I. To evaluate overall response rate CR \& PR(Complete Response + Partial Response)as assessed by RECIST (Response Evaluation Criteria in Solid Tumors v 1.1) of the combination of pralatrexate and docetaxel in patients with advanced esophageal and gastroesophageal carcinomas.

SECONDARY OBJECTIVES:

I. Evaluation of progression free survival and overall survival. II. Correlation of FDG(fludeoxyglucose)PET(positron emission tomography)response defined as a 35% reduction in SUV(standard uptake value)during the early course of chemotherapy to progression free and overall survival in addition to radiographic response as measured by RECIST v 1.1 criteria on CT imaging.

OUTLINE:

Patients receive pralatrexate IV over 3-5 minutes and docetaxel IV on day 1. Courses repeat every 14 days in the absence of disease progression or unacceptable toxicity.

Eligibility Criteria:
Inclusion

* Pathologically confirmed unresectable advanced or metastatic carcinoma of the esophagus or gastroesophageal junction
* Established histological confirmation of squamous cell carcinoma or adenocarcinoma of the esophagus or gastroesophageal junction
* Stage IV disease
* Must have received platinum-based therapy; this includes definitive, adjuvant and metastatic treatments
* No more than 3 chemotherapeutic treatment regimens permitted; this includes concurrent chemoradiation
* Radiation therapy allowed if \> 4 weeks have elapsed
* Must be off therapy for 4 weeks prior to enrollment
* Measurable disease as defined by RECIST v 1.1 criteria
* ECOG (Eastern Cooperative Oncology Group)PS(Performance status)of 0 to 2
* Predicted life expectancy of at least 12 weeks
* Patients with reproductive potential must use an effective method to avoid pregnancy for the duration of the trial and for three months after completion of treatment
* Marrow: ANC(absolute neutrophil count)\> 1,000/mm\^3
* Marrow: Hemoglobin \> 9.0 g/dl
* Marrow: Platelet Count \> 100,000/mm\^3
* Renal: Serum creatinine =\< 1.5 g/dL
* Hepatic: Serum bilirubin \< 1.5 x ULN(upper limit of normal) and AST (aspartate aminotransferase) and ALT (Alanine aminotransferase)=\< 2.5 x ULN
* Prior minor surgeries (such as laparoscopies) must have occurred at least 14 days prior to study enrollment; prior minor procedures such as biopsies and mediport placement must have occurred at least 48 hours prior to study enrollment
* All patients must have signed an informed consent indicating that they are aware of the neoplastic nature of their disease and have been informed of the procedures of the protocol, the experimental nature of the therapy, alternatives, potential benefits, side effects, risks, and discomforts
* History of allergic reactions attributed to compounds of similar chemical composition to agents used in the study

Exclusion

* Pregnant or lactating women
* Patients with any severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for study entry
* Any malignant condition for which one has received treatment in the last two years excluding squamous or basal cell carcinomas
* Patients with untreated brain metastases
* Patients must not have grade 2 or higher baseline peripheral neuropathy, according to CTCAE v 4.0
* Patients must have NO continuing acute toxic effects (except alopecia) of any prior radiotherapy, chemotherapy, or surgical procedures; all such effects must have resolved to Common Terminology Criteria for Adverse Events (CTCAE v 4.0) Grade =\< 1 prior to study enrollment