Vaccine Therapy in Treating Patients With Stage IV HLA-A2 and HER2 Positive Breast or Ovarian Cancer Receiving Trastuzumab

Inclusion Criteria: * Subjects must have either stage IV breast or ovarian cancer in remission or with stable disease on trastuzumab monotherapy * HER2 overexpression by immunohistocytochemistry (IHC) of 2+ or 3+, in the primary tumor or metastasis; if overexpression is 2+ by IHC, then patients must have HER2 gene amplification documented by fluorescence in situ hybridization (FISH) * Subjects must be HLA-A2 positive * Eligible subjects must have completed appropriate treatment for their primary disease and be off cytotoxic chemotherapy and any immunosuppressive agents such as systemic steroids for at least 30 days prior to enrollment; patients should continue trastuzumab monotherapy throughout the course of this protocol; concurrent hormonal and biphosphonate therapies are allowed * Subjects must have an Eastern Cooperative Oncology Group (ECOG) performance status score = 0 or 1 * Male subjects must agree to contraceptive use during the study period (7 months) and non-menopausal female subjects must agree to contraception for the remainder of their childbearing years * Hematocrit \>= 30 performed within 60 days of enrollment * Platelet count \>= 100,000 performed within 60 days of enrollment * White blood cells (WBC) \>= 3000/ul performed within 60 days of enrollment * Stable creatinine =\< 2.0 mg/dL or creatinine clearance \>= 60 ml/min performed within 60 days of enrollment * Serum bilirubin \< 1.5 mg/dl performed within 60 days of enrollment * Serum glutamic-oxaloacetic …