This randomized clinical trial is studying the side effects of oregovomab and to see how well it works with or without cyclophosphamide in treating patients with stage III or stage IV ovarian epithelial cancer, fallopian tube cancer, or primary peritoneal cancer that responded to second-line chemotherapy. Monoclonal antibodies, such as oregovomab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Drugs used in chemotherapy, such as cyclophosphamide, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. It is not yet known whether oregovomab is more effective when given together with or without cyclophosphamide in treating patients with stage III or stage IV ovarian epithelial cancer, fallopian tube cancer, or primary peritoneal cancer.

PRIMARY OBJECTIVES:

I. To characterize the nonspecific humoral immune response, as measured by human anti-murine antibodies (HAMA), in patients with stage III or IV ovarian epithelial, fallopian tube, or primary peritoneal adenocarcinoma treated with consolidation therapy comprising adjuvant oregovomab with vs without cyclophosphamide after achieving a complete clinical response to second-line taxane/platinum-based therapy.

II. To compare the magnitude of the immune responses in these patients at approximately 14 weeks after the initial treatment.

III. To determine the frequency and severity of adverse events, as assessed by NCI CTCAE v3.0, in patients treated with these regimens.

SECONDARY OBJECTIVES:

I. To characterize the specific humoral immune response, as measured by HAMA and anti-idiotype antibodies, in these patients.

II. To assess the treatment emergent cellular immune response, by measuring the delayed-type hypersensitivity response to the anergy panel and to oregovomab as compared to baseline, in these patients.

III. To characterize the duration of each patient's first progression-free interval after primary chemotherapy and second progression-free interval after another regimen of chemotherapy.

OUTLINE: This is a multicenter study. Patients are randomized to 1 of 2 treatment arms.

ARM I: Patients undergo delayed-type hypersensitivity (DTH) skin testing with oregovomab and a standard anergy panel (i.e., mumps, Candida, and tetanus toxoid) on day 0 (at baseline) and at week 14. The skin test response is measured 48 hours later. Patients receive cyclophosphamide IV on day 6 and oregovomab IV over 20 minutes on day 9 or 10. Patients then receive oregovomab alone at weeks 6 and 10 and then every 12 weeks for up to 2 years (10 doses) in the absence of disease progression or unacceptable toxicity.

ARM II: Patients undergo DTH skin testing and receive oregovomab as in arm I.

Blood samples are obtained from patients at baseline and at weeks 14 and 38 for immunologic correlative studies. Samples are examined to determine CA-125 levels and human anti-murine antibody (HAMA) and anti-idiotype antibody levels by enzyme-linked immunosorbent assay (ELISA).

After completion of study therapy, patients are followed every 3 months for 2 years and then every 6 months for 3 years.

Criteria:

• Histologically confirmed ovarian epithelial, fallopian tube, or primary peritoneal adenocarcinoma
• Histologic documentation of the original primary tumor is required via pathology report
• FIGO stage III-IV disease
• Must have received 5-8 courses of front-line taxane- and platinum-based chemotherapy OR treatment on a first-line Gynecologic Oncology Group (GOG) protocol AND must have become clinically free of disease as measured by serum CA-125 level, CT scan, or physical examination
• Must have documentation of a defined progression-free interval after front-line therapy, as measured from the date of initiation of front-line chemotherapy to the date of initiation of second-line chemotherapy
• Relapsed disease (prior to starting second-line chemotherapy), defined by 1 of the following: doubling of serum CA-125 level confirmed by measurements taken 1 week apart (CA-125 level should have been elevated to at least double the level seen during the first complete response); identification of a new lesion by CT/MRI scan or physical examination
• Must have completed 5-8 courses of second-line taxane- and platinum-based chemotherapy 4-8 weeks ago
• Second-line chemotherapy must not have been started before clear evidence of disease recurrence was documented using RECIST criteria
• Achieved complete clinical response to second-line chemotherapy with no symptoms suggestive of persistent disease, defined by the following: normal physical examination; reduction from the peak serum CA-125 level to a normal value of >= 5 U/mL; complete regression of recurrent lesions by CT scan of the abdomen/pelvis
• No low malignant potential tumors or noninvasive disease
• GOG performance status 0-1
• ANC >= 1,500/mm^3
• Platelet count >= 100,000/mm^3
• Hemoglobin >= 8.0 g/dL
• Creatinine =< 1.5 times upper limit of normal (ULN)
• Bilirubin =< 1.5 times ULN
• AST =< 2.5 times ULN
• Alkaline phosphatase =< 2.5 times ULN
• No known allergy to murine proteins, documented anaphylactic reaction to any drug, or intolerance to cyclophosphamide
• No active autoimmune disease (e.g., rheumatoid arthritis, systemic lupus erythematosus, ulcerative colitis, Crohn's disease, multiple sclerosis, or ankylosing spondylitis)
• No recognized immunodeficiency disease, including cellular immunodeficiencies, hypogammaglobulinemia, or dysgammaglobulinemia
• No acquired, hereditary, or congenital immunodeficiencies
• No other concurrent uncontrolled diseases
• No contraindications to pressor agents
• No other invasive malignancies within the past 5 years, except nonmelanoma skin cancer
• No prior cancer treatment that would contraindicate study therapy
• No concurrent chronic treatment with immunosuppressive drugs (e.g., cyclosporine, adrenocorticotropic hormone [ACTH], or systemic corticosteroids)