This phase II trial studies the side effects of giving bortezomib together with vorinostat and to see how well it works in treating patients with multiple myeloma who have undergone autologous stem cell transplant. Bortezomib and vorinostat may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Giving bortezomib together with vorinostat after an autologous stem cell transplant may stop the growth of any cancer cells that remain after transplant.