This randomized phase II trial studies abiraterone acetate and prednisone together with veliparib to see how well it works compared to abiraterone acetate and prednisone alone in treating patients with castration-resistant prostate cancer that has spread from the primary site to other places in the body. Androgens can cause the growth of prostate cancer cells. Antiandrogen drugs, such as abiraterone acetate, may lessen the amount of androgens made by the body. Veliparib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Giving abiraterone acetate together with prednisone and veliparib may work better than abiraterone acetate and prednisone alone in treating patients with castration-resistant prostate cancer.