Vaccine Therapy, Paclitaxel, and Carboplatin in Treating Patients Who Are Undergoing Surgery for Stage III or Stage IV Ovarian Cancer, Primary Peritoneal Cancer, or Fallopian Tube Cancer

RATIONALE: Vaccines made from peptides may help the body build an effective immune response to kill tumor cells. Drugs used in chemotherapy, such as paclitaxel and carboplatin, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving chemotherapy before surgery may make the tumor smaller and reduce the amount of normal tissue that needs to be removed. Giving vaccine therapy and chemotherapy after surgery may kill any tumor cells that remain after surgery. PURPOSE: This phase II trial is studying how well giving vaccine therapy together with paclitaxel and carboplatin works in treating patients who are undergoing surgery for stage III or stage IV ovarian cancer, primary peritoneal cancer, or fallopian tube cancer.

OBJECTIVES: * Determine the immunogenicity of vaccine therapy comprising synthetic ovarian cancer-associated peptides administered with a synthetic tetanus toxoid helper peptide emulsified in Montanide ISA-51 before or after paclitaxel and carboplatin in patients with stage III-IV ovarian epithelial, primary peritoneal cavity, or fallopian tube cancer undergoing optimal cytoreductive surgery. OUTLINE: This is an open-label study. Patients are assigned to 1 of 2 treatment groups. * Group 1: * Neoadjuvant chemotherapy:Patients receive paclitaxel IV over 3 hours and carboplatin IV over 30 minutes on day 1. Treatment repeats every 21 days for up to 4 courses in the absence of disease progression or unacceptable toxicity. Patients then proceed to surgical debulking. * Surgical debulking: Patients undergo primary optimal cytoreductive surgery. * Vaccine therapy: Within 14 days after surgery, patients receive vaccine therapy comprising synthetic ovarian cancer-associated peptides, MAGE-A1:161-169, FBP:1901-199, Her-2/neu:369-377, MAGE-A1:96-104, and Her-2/neu:754-762, and tetanus toxoid helper peptide emulsified in Montanide ISA-51 intradermally and subcutaneously on days 1, 8, and 15. Treatment repeats every 14 weeks for 2 courses. * Adjuvant chemotherapy: Patients receive 4 courses of paclitaxel and carboplatin as in neoadjuvant chemotherapy after completion of course 1 of vaccine therapy. * Group 2: * Surgical debulking: Patients undergo up-front optimal cytoreductive surgery. Patients with non-optimal primary debulking may undergo interval debulking surgery within 6 weeks after completing course 4 of adjuvant chemotherapy. If interval debulking surgery is performed, tumor and/or lymph node tissue is collected. * Vaccine therapy: Patients receive 2 courses of vaccine therapy as in group 1. * Adjuvant chemotherapy: Patients receive paclitaxel and carboplatin as in group 1, neoadjuvant chemotherapy. Treatment repeats every 21 days for up to 8 courses. Patients undergo periodic blood and tumor tissue collection during study for correlative immunological analysis. After completion of study treatment, patients with progressive disease are followed at 30 days and then every six months thereafter. All other patients are followed every 3 months for 36 months until disease progression or until another therapy is initiated, and then every six months thereafter. PROJECTED ACCRUAL: A total of 28 patients will be accrued for this study.