 This phase I clinical trial studies the side effects of sirolimus and NY-ESO-1 protein with MIS416 in treating patients stage II-IV ovarian, fallopian tube, or primary peritoneal cancer. Sirolimus may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Vaccine therapy, like Y-ESO-1 protein with MIS416, may strengthen the immune system to find and kill tumor cells. Biological therapies, such as sirolimus, use substances made from living organisms that may stimulate or suppress the immune system in different ways and stop tumor cells from growing. Giving sirolimus and vaccine therapy may work betting in treating patients with ovarian, fallopian tube or primary peritoneal cancer. 