Sirolimus and Vaccine Therapy in Treating Patients With Stage II-IV Ovarian Epithelial, Fallopian Tube, or Primary Peritoneal Cavity Cancer

Inclusion Criteria:

* Eligible patients will be women with stages II-IV epithelial ovarian, fallopian tube, or primary peritoneal carcinoma who have completed standard therapy for primary or recurrent disease (i.e., patients who would normally be observed); eligible patients may have asymptomatic residual measurable disease on physical examination and/or computed tomography (CT) scan, and/or may have an elevated cancer antigen 125 (CA-125); or may be in complete clinical remission after treatment for primary or recurrent disease; these patients would normally enter a period of observation after standard management
* Any human leukocyte antigen (HLA) type; (historic HLA typing is permitted)
* Tumor expression of NY-ESO-1 or cancer/testis antigen 2 (LAGE-1) by immunohistochemistry (IHC) and/or real-time polymerase chain reaction (RT-PCR)
* No allergy to eggs
* Life expectancy \> 6 months
* Hematology and biochemistry laboratory results within the limits normally expected for the patient population, without evidence of major organ failure
* Absolute neutrophil count (ANC) \>= 1,000/uL
* Platelet \>= 75,000/uL
* Hemoglobin (Hgb) \>= 8 g/dL
* Total bilirubin =\< 1.5 x upper limit of normal (ULN)
* Serum glutamic oxaloacetic transaminase (SGOT)/aspartate aminotransferase (AST) or serum glutamic pyruvic transaminase (SGPT)/alanine aminotransferase (ALT) =\< 3 x ULN
* Serum creatinine =\< 2 x ULN
* Prothrombin time (PT)/international normalized ratio (INR) =\< 1.5
* Electrocardiogram, showing no evidence of congestive heart failure, myocardial infarction, and cardiomyopathy
* Have been informed of other treatment options
* Patient or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure
* Have an Eastern Cooperative Oncology Group (ECOG) Performance Status of =\< 2
* Demonstrate the ability to swallow and retain oral medication
* Patients of child-bearing potential must agree to use acceptable contraceptive methods (e.g., double barrier) during treatment
* Patients may have received previous NY-ESO-1 vaccine therapy

Exclusion Criteria:

* Metastatic disease to the central nervous system for which other therapeutic options, including radiotherapy, may be available
* Other serious illnesses (e.g. serious infections requiring antibiotics, bleeding disorders)
* History of severe autoimmune disorders requiring use of steroids or other immunosuppressives
* Concomitant systemic treatment with corticosteroids, anti-histamine or nonsteroidal anti-inflammatory drugs and other platelet inhibitory agents, strong inhibitors/inducers of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP450-3A4)
* Chemotherapy, radiation therapy, or immunotherapy within 4 weeks prior to first dosing of study drug (6 weeks for nitrosoureas); concomitant hormonal therapies for breast cancers are allowed
* Known allergy or history of life threatening reaction to GM-CSF
* Clinically significant heart disease (N-YHA Class III or IV)
* Participation in any other clinical trial involving another investigational agent within 4 weeks prior to first dosing of study drug
* Known hepatitis B, hepatitis C, or HIV
* Mental impairment that may compromise the ability to give informed consent and comply with the requirements of the study
* Lack of availability of a patient for immunological and clinical follow-up assessment
* Known pulmonary hypertension
* Known hypersensitivity to sirolimus
* Evidence of current drug or alcohol abuse or psychiatric impairment, which in the investigator's opinion will prevent completion of the protocol therapy or follow-up
* Pregnant or nursing female patients
* Unwilling or unable to follow protocol requirements
* Any condition which in the investigator's opinion deems the patient an unsuitable candidate to receive study drug; (i.e., any significant medical illness or abnormal laboratory finding that would, in the investigator's judgment, increase the subject's risk by participating in this study)