Future embedded real-time systems will be deployed on multi-core processors to meet the dramatically increasing high-performance and low-power requirements. This trend appeals to generalize established results on uniprocessor scheduling, particularly the various utilization bounds for schedulability test used in system design, to the multiprocessor setting. Recently, this has been achieved for the famous Liu and Lay land utilization bound by applying novel task splitting techniques. However, parametric utilization bounds that can guarantee higher utilizations (up to 100%) for common classes of systems are not yet known to be generalizable to multiprocessors as well. In this paper, we solve this problem for most parametric utilization bounds by proposing new task partitioning algorithms based on exact response time analysis. In addition to the worst-case guarantees, as the exact response time analysis is used for task partitioning, our algorithms significantly improve average-case utilization over previous work.