OPT-821 With or Without Vaccine Therapy in Treating Patients With Ovarian Epithelial Cancer, Fallopian Tube Cancer, or Peritoneal Cancer in Second or Third Complete Remission

PRIMARY OBJECTIVES: I. To determine if a polyvalent vaccine (including GM2-keyhole limpet hemocyanin \[KLH\], Globo-H-KLH, Tn-mucin 1 \[MUC1\]-32mer-KLH, and Thompson Friedreich antigen \[TF\]-KLH plus OPT-821) decreases the hazard of progression or death compared to a vaccine containing OPT-821 alone in women with epithelial ovarian, fallopian tube, or peritoneal cancer in second or third complete clinical remission. SECONDARY OBJECTIVES: I. To compare the treatment arms with respect to the incidence of toxicities. II. To determine if the polyvalent vaccine decreases the hazard of death compared to a vaccine containing OPT-821 alone in women with epithelial ovarian, fallopian tube, or peritoneal cancer in second or third complete clinical remission. TERTIARY OBJECTIVES: I. To evaluate the immune response (by enzyme linked immunosorbent assay \[ELISA\]) in participants, in order to determine if the outcome correlates with antigen-specific immune titers. OUTLINE: Patients are randomized to 1 of 2 treatment arms. ARM I: Patients receive polyvalent antigen-KLH conjugate vaccine and immunological adjuvant OPT-821 subcutaneously (SC) once in weeks 1, 2, 3, 7, 11, 23, 35, 47, 59, 71, and 83 in the absence of disease progression or unacceptable toxicity. ARM II: Patients receive immunological adjuvant OPT-821 SC as in Arm I. After completion of study treatment, patients are followed up every 3 months for 2 years, every 6 months for 3 years, and then annually thereafter.