Inclusion Criteria:

   - Life expectancy >= 12 weeks

   - Women 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

   - Women of child-bearing potential and men must agree to use adequate contraception
   (hormonal or barrier method or birth control; abstinence) for the duration of study
   therapy and for 3 months after the last dose of cixutumumab (IMC-A12); should a woman
   become pregnant or suspect she is pregnant while participating in this study, she
   should inform her treating physician immediately

   - Patients must have measurable disease

   - Patients 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 is also permitted

      - For the purposes of this study, undifferentiated adenocarcinomas and
      adenosquamous tumors will be considered as adenocarcinomas; in addition, tumors
      involving the gastroesophageal junction will be defined by the Siewert
      classification

   - Patients with gastroesophageal junction tumors who 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

   - Patients with gastroesophageal junction tumors who are NOT eligible:

      - AEG Type III: subcardial gastric carcinoma which infiltrates the esophagogastric
      junction and distal esophagus from below

   - Patients must have received and progressed on one and only one line of prior systemic
   therapy for esophagus or esophagogastric cancer; this could have included one regimen
   for metastatic disease, or one regimen with radiotherapy for initially locally
   advanced disease; prior radiation therapy is permitted

      - 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 one line of
      therapy; however, 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

   - Patients 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; patients are not considered to have a "currently active" malignancy if
   they have completed therapy and are considered by their physician to be at less than
   30% risk of relapse

Exclusion Criteria:

   - Patients have received prior taxane or anti-insulin growth factor receptor (IGFR)
   therapy

   - Patients must not have any of the following conditions:

      - Poorly controlled diabetes mellitus; patients with a history of diabetes mellitus
      are allowed to participate, provided that their 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 they are on 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