In practice, many types of manipulation actions (e.g., pick-n-place and push) are needed to accomplish real-world manipulation tasks. Yet, limited research exists that explores the synergistic integration of different manipulation actions for optimally solving long-horizon task-and-motion planning problems. In this study, we propose and investigate planning high-quality action sequences for solving long-horizon tabletop rearrangement tasks in which multiple manipulation primitives are required. Denoting the problem rearrangement with multiple manipulation primitives (REMP), we develop two algorithms, hierarchical best-first search (HBFS) and parallel Monte Carlo tree search for multi-primitive rearrangement (PMMR) toward optimally resolving the challenge. Extensive simulation and real robot experiments demonstrate that both methods effectively tackle REMP, with HBFS excelling in planning speed and PMMR producing human-like, high-quality solutions with a nearly 100% success rate.