Oregovomab 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

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)