This phase I trial studies the side effects and best dose of selinexor and carfilzomib when given together with dexamethasone in treating patients with multiple myeloma that has returned or does not respond to treatment. Drugs used in chemotherapy, such as selinexor 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. Carfilzomib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Giving selinexor, carfilzomib, and dexamethasone may be a better treatment for multiple myeloma.