This randomized phase II trial studies how well abiraterone acetate and antiandrogen therapy, with or without cabazitaxel and prednisone, work in treating patients with castration-resistant prostate cancer previously treated with docetaxel that has spread to other parts of the body. Androgens can cause the growth of prostate cancer cells. Hormone therapy using abiraterone acetate and antiandrogen therapy may fight prostate cancer by lowering and/or blocking the use of androgens by the tumor cells. Drugs used in chemotherapy, such as cabazitaxel and prednisone, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving abiraterone acetate and antiandrogen therapy with or without cabazitaxel and prednisone may help kill more tumor cells.