Inclusion Criteria:

          -  Pathologically confirmed primary adenocarcinoma of the esophagus that involves the mid
             (up to 25 cm), distal, or esophagogastric junction; the cancer may involve the stomach
             up to 5 cm

          -  Endoscopy with biopsy

          -  PRIOR TO STEP 1 REGISTRATION BUT WITHIN 56 DAYS PRIOR TO STEP 2 REGISTRATION

          -  Intent to submit tissue for central HER2 testing

          -  Stage T1N1-2, T2-3N0-2, according to the American Joint Committee on Cancer (AJCC) 7th
             edition staging, based on the following minimum diagnostic work-up:

               -  Chest/abdominal/pelvic computed tomography (CT) or whole-body positron emission
                  tomography (PET)/CT (NOTE: if CT is performed at this time point, whole-body
                  PET/CT will be required prior to step 2 registration; PET/CT of skull base to
                  mid-thigh is acceptable) (NOTE: if adenopathy is noted on CT or whole-body PET/CT
                  scan, an endoscopic ultrasound is not required prior to STEP 2 registration as
                  long as adequate tissue has been obtained for central HER2 testing)

               -  Patients may have regional adenopathy including para-esophageal, gastric,
                  gastrohepatic and celiac nodes; if celiac adenopathy is present, it must be =< 2
                  cm

               -  Patients with tumors at the level of the carina or above must undergo
                  bronchoscopy to exclude fistula

          -  Zubrod performance status 0-2

          -  Absolute neutrophil count (ANC) >= 1,500 cells/mm^3

          -  Platelets >= 100,000 cells/mm^3

          -  Hemoglobin >= 8.0 g/dL (note: the use of transfusion or other intervention to achieve
             hemoglobin [Hgb] >= 8.0 g/dL is acceptable)

          -  Creatinine =< 2 times upper limit of normal

          -  Bilirubin =< 1.5 times upper limit of normal

          -  Aspartate aminotransferase (AST) =< 3.0 times upper limit of normal

          -  For women of childbearing potential, a negative serum or urine pregnancy test

          -  Patients must sign a study-specific informed consent prior to study entry

          -  CONDITIONS FOR PATIENT ELIGIBILITY PRIOR TO STEP 2 REGISTRATION (HER2-POSITIVE
             PATIENTS ONLY)

          -  HER2 expressing adenocarcinoma of the esophagus centrally

          -  Surgical consultation to confirm that patient will be able to undergo curative
             resection after completion of chemoradiation within 56 days prior to step 2
             registration

          -  Radiation oncology consultation to confirm that disease can be encompassed in a
             radiotherapy field within 56 days prior to step 2 registration

          -  Consultation with a medical oncologist within 56 days prior to step 2 registration

          -  Stage T1N1-2, T2-3N0-2, according to the AJCC 7th edition staging, based upon the
             following minimum diagnostic work-up:

               -  History/physical examination, with documentation of the patient's weight, within
                  14 days prior to step 2 registration

               -  Whole-body PET/CT scan within 56 days prior to step 2 registration (if only CT
                  performed prior to step 1 registration)

               -  Endoscopic ultrasound within 56 days prior to step 2 registration, unless the
                  patient is found to have adenopathy per CT or whole-body PET/CT scan

               -  Electrocardiogram (EKG) within 56 days prior to step 2 registration

               -  Serum creatinine =< 2 x the upper limit or normal within 14 days prior to step 2
                  registration

          -  Zubrod performance status 0-2 within 14 days prior to step 2 registration

          -  For women of childbearing potential, a negative serum pregnancy test within 14 days
             prior to step 2 registration

          -  Left ventricular ejection fraction (LVEF) >= institutional lower limit of normal by
             cardiac echocardiogram (echo) or multi gated acquisition (MUGA) scan within 56 days
             prior to step 2 registration

          -  Women of childbearing potential and sexually active male participants must agree to
             practice adequate contraception while on study and for at least 60 days following the
             last dose of chemotherapy or trastuzumab

        Exclusion Criteria:

          -  Patients with cervical esophageal carcinoma

          -  Patients with T1N0 disease, T4 disease, and proximal esophageal cancers (15-24 cm)

          -  Prior systemic chemotherapy for esophageal cancer; note that prior chemotherapy for a
             different cancer is allowable

          -  Prior radiation therapy for esophageal cancer or prior chest radiotherapy

          -  Prior anthracycline or taxane

          -  Evidence of tracheoesophageal fistula or invasion into the trachea or major bronchi

          -  Prior invasive malignancy (except non-melanomatous skin cancer), unless disease free
             for a minimum of 2 years (e.g., carcinoma in situ of the breast, oral cavity, or
             cervix are permissible)

          -  Medical contraindications to esophagectomy

          -  Prior therapy with any agent targeting the HER2 pathway or human epidermal growth
             factor receptor 1 (HER1) (epidermal growth factor receptor [EGFR]) pathway

          -  Prior therapy with trastuzumab

          -  Prior allergic reaction to the study drugs involved in this protocol or to a
             monoclonal antibody

          -  Previous history of congestive heart failure

          -  Severe, active comorbidity, defined as follows:

               -  Unstable angina in the last 6 months

               -  Transmural myocardial infarction within the last 6 months

               -  Acute bacterial or fungal infection requiring intravenous antibiotics at the time
                  of registration

               -  Acquired immune deficiency syndrome (AIDS) based upon current Centers for Disease
                  Control and Prevention (CDC) definition; note, however that human
                  immunodeficiency virus (HIV) testing is not required for entry into this
                  protocol; protocol-specific requirements may also exclude immunocompromised
                  patients

          -  Pregnant or nursing women or women of childbearing potential and men who are sexually
             active and not willing/able to use medically acceptable forms of contraception