This phase I trial studies the side effects and best dose and schedule of sirolimus when given together with vaccine therapy in treating patients with stage II-IV ovarian epithelial, fallopian tube, or primary peritoneal cavity cancer. Sirolimus may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Vaccines made from a gene-modified virus may help the body build an effective immune response to kill tumor cells. Giving vaccine therapy together with sirolimus may be an effective treatment for ovarian, fallopian tube, or primary peritoneal cancer
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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)