Inclusion Criteria

• Life expectancy ≥ 12 weeks
• Must not be pregnant or breast-feeding due to potential harm to fetus from cixutumumab (IMC-A12) and paclitaxel
• All females of childbearing potential must have a blood test or urine study within 48 hours prior to registration to rule out pregnancy
• Females of child-bearing potential and men must agree to use adequate contraception (hormonal, barrier method or birth control, or abstinence) for the duration of study therapy and for 3 months after the last dose of cixutumumab (IMC-A12)
  • If a woman becomes pregnant or suspects she is pregnant while participating in this study, she should inform her treating physician immediately
• Must have measurable disease
• Must have metastatic disease of the esophagus or gastroesophageal junction
  • Histologic, cytologic or radiologic documentation of metastatic squamous cell carcinoma or adenocarcinoma of the esophagus or gastroesophageal junction
  • Radiologic, endoscopic, histologic or cytologic evidence of locally recurrent or locally residual (post-resection) disease
  • For the purposes of this study
    • Undifferentiated adenocarcinomas and adenosquamous tumors will be considered as adenocarcinomas
    • Tumors involving the gastroesophageal junction will be defined by the Siewert classification
  • Gastroesophageal junction tumors that are eligible
    • Adenocarcinoma of the esophageal junction (AEG) Type I
      • Adenocarcinoma of the distal esophagus which usually arises from an area with specialized intestinal metaplasia of the esophagus, i.e., Barrett's 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
  • Gastroesophageal junction tumors that are NOT eligible
    • AEG Type III
      • Subcardial gastric carcinoma which infiltrates the esophagogastric junction and distal esophagus from below
  • Must have received and progressed on one and only one line of prior systemic therapy for esophagus or esophagogastric cancer
  • Could have included one regimen for metastatic disease, or one regimen with radiotherapy for initially locally advanced disease
  • Prior radiation therapy is permitted
    • For progress or recurrance within 6 months of neoadjuvant/adjuvant therapy this will be considered one line of therapy
    • For progression or recurrance more than 6 months after neoadjuvant/adjuvant therapy will need to receive one line of therapy for the recurrent disease
    • If receive one regimen in which a chemotherapy agent is dropped for toxicity without progression, this treatment will be considered one line of therapy
    • Substitution or addition of a new agent will be considered a second line of therapy
• Eastern Cooperative Oncology Group (ECOG) performance status 0-2
• Leukocytes > 3,000/mcL
• Absolute neutrophil count ≥ 1,500/mcL
• Hemoglobin ≥ 9 g/dL
• Platelets ≥ 100,000/mcL
• Total bilirubin ≤ institutional upper limit of normal (ULN)
• Aspartate transaminase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine transaminase (ALT) (serum glutamate pyruvate transaminase [SGPT]) ≤ 3 X institutional ULN
• Creatinine ≤ 1.5 X institutional ULN or creatinine clearance ≥ 60 mL/min/1.73m^2 for patients with creatinine levels above institutional normal
• Must have fasting serum glucose ≤ 160 mg/dL (8.8 mmol/L) or ≤ ULN, and hemoglobin A1C ≤ 7% (0.07 International System of Units [SI units]) within 14 days of registration
  • If baseline nonfasting glucose ≤ 160 mg/dL (8.8 mmol/L), fasting glucose measurement is not required
• Registration no fewer than 28 days from last chemotherapy
• A currently active second malignancy other than non-melanoma skin cancers are not to be registered
  • Not considered to have a currently active malignancy if have completed therapy and are considered by their physician to be at less than 30% risk of relapse

Exclusion Criteria

• Has received prior taxane or anti-insulin growth factor receptor (IGFR) therapy
• Must not have any of the following conditions
  • Poorly controlled diabetes mellitus
    • History of diabetes mellitus allowed provided blood glucose is within normal range (fasting glucose ≤ 160 mg/dL [8.8 mmol/L] or below the ULN and hemoglobin A1C ≤ 7% [0.07 SI units]) and that there is a stable dietary or therapeutic regimen for this condition
  • Recent major surgery, hormonal therapy (other than replacement) or chemotherapy, within 4 weeks prior to entering the study or those who have not recovered from adverse events
  • History of allergic reactions attributed to compounds of similar chemical or biologic composition to cixutumumab (IMC-A12)
  • Psychiatric illness that would prevent the patient from giving informed consent
  • Medical conditions such as active/uncontrolled infection (including HIV) or cardiac disease that would make this protocol unreasonably hazardous for the patient in the opinion of the treating physician
    • Cardiac disease may include uncontrolled high blood pressure, unstable angina, or serious uncontrolled cardiac arrhythmia