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

PRIMARY OBJECTIVE: I. Determine the safety and feasibility of NY-ESO-1 protein with MIS416 in combination with mammalian target of rapamycin (mTOR) inhibitor sirolimus. SECONDARY OBJECTIVES: I. To determine the effectiveness of these combinatorial therapies by assessing NY-ESO-1 specific cellular and humoral immunity: peripheral blood NY-ESO-1 specific cluster of differentiation (CD)8+ and CD4+ T-cells; peripheral blood NY-ESO-1 specific antibodies; peripheral blood frequency of CD4+ CD25+ forkhead box P3 (FOXP3)+ regulatory T-cells; explore time to disease progression. OUTLINE: COHORT I (C1): Patients receive NY-ESO-1 protein with MIS416 vaccine subcutaneously (SC) on days 1, 15, 29, 57, 85, and 113 in the absence of disease progression or toxicity. COHORT II (C2): Patients receive NY-ESO-1 protein with MIS416 vaccine as in Cohort I. Patients also receive sirolimus orally (PO) daily for 2 weeks followed by 2 weeks off starting on days 1, 29, 57, and 85. After completion of study treatment, patients are followed up at 30 days and then at 12 months.