This pilot clinical trial studies how well ixazomib citrate, lenalidomide, and dexamethasone work in treating patients with polyneuropathy, organomegaly, endocrinopathy, monoclonal gammopathy, and skin changes (POEMS) syndrome. Ixazomib citrate may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as lenalidomide and dexamethasone, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving ixazomib citrate, lenalidomide, and dexamethasone may work better in treating patients with POEMS syndrome.