Inclusion Criteria:

- Histologically, cytologically, or radiologically confirmed metastatic esophageal or
gastroesophageal junction meeting 1 of the following criteria:

- Squamous cell carcinoma

- Adenocarcinoma

- Undifferentiated adenocarcinomas and adenosquamous tumors will be
considered as adenocarcinomas

- Patients with adenocarcinoma of the gastroesophageal or esophagogastric (AEG)
junction tumors meeting the following:

- AEG type I: adenocarcinoma of the distal esophagus that usually arises from an
area with specialized intestinal metaplasia of the esophagus (i.e., Barrett
esophagus) and may infiltrate the esophagogastric junction from above

- AEG type II: true carcinoma of the cardia arising from the cardiac epithelium or
short segments with intestinal metaplasia at the esophagogastric junction

- No AEG type III: subcardial gastric carcinoma that infiltrates the
esophagogastric junction and distal esophagus from below

- Evidence of local recurrence or local residual (post-resection) disease by radiology,
endoscopy, histology, or cytology allowed

- Measurable disease

- Must have received and progressed on 1 line of prior systemic therapy for esophageal
or esophagogastric cancer meeting ≥ 1 of the following criteria:

- May have included one regimen for metastatic disease, or one regimen with
radiotherapy for initially locally advanced disease

- If patients progress or recur within 6 months of neoadjuvant/adjuvant therapy,
this will be considered one line of therapy

- For patients progressing or recurring more than 6 months after
neoadjuvant/adjuvant therapy, they will need to receive one line of therapy
for recurrent disease to be eligible

- If patients receive one regimen in which a chemotherapy agent is dropped for
toxicity without progression, this treatment will be considered 1 line of
therapy

- Substitution or addition of a new agent will be considered a second line of
therapy

- ECOG performance status 0-2

- Life expectancy ≥ 12 weeks

- Leukocytes ≥ 3,000/mm^3

- ANC ≥ 1,500/mm^3

- Platelet count ≥ 100,000/mm^3

- Hemoglobin ≥ 9 g/dL

- Total bilirubin normal

- AST and/or ALT ≤ 3 times upper limit of normal (ULN)

- Creatinine ≤ 1.5 times ULN OR creatinine clearance ≥ 60 mL/min

- Fasting serum glucose ≤ 160 mg/dL and hemoglobin A_1C ≤ 7%

- Fasting glucose not required if non-fasting glucose ≤ 160 mg/dL

- History of diabetes mellitus allowed provided blood glucose is within normal
range and patients are on a stable dietary or therapeutic regimen

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception during and for 3 months after
completion of study therapy

- No history of allergic reactions attributed to compounds of similar chemical or
biologic composition to cixutumumab

- No psychiatric illness that would prevent the patient from giving informed consent

- None of the following medical conditions that, in the opinion of the treating
physician, would make this protocol unreasonably hazardous for the patient

- Active and/or uncontrolled infection, including HIV positivity

- Cardiac disease including, but not limited to, any of the following:

- Uncontrolled high-blood pressure

- Unstable angina

- Serious uncontrolled cardiac arrhythmia

- No currently active second malignancy except nonmelanoma skin cancer or curatively
treated malignancy with < 30% risk of relapse

- No prior treatment with other agents targeting the IGFR

- More than 4 weeks since prior major surgery, hormonal therapy (other than
replacement), or chemotherapy and recovered

- No prior taxane or anti-IGFR therapy