This partially randomized phase I/II trial studies the side effects and best dose of enzalutamide and mifepristone when given together and to see how well they work in treating patients with metastatic hormone resistant prostate cancer. Androgens can cause the growth of prostate cancer cells. Antihormone therapy, such as enzalutamide and mifepristone, may lessen the amount of androgens made by the body. It is not yet known whether enzalutamide is more effective with or without mifepristone in treating patients with prostate cancer.