Transactional Stream Processing Engines (TSPEs) form the backbone of modern stream applications handling shared mutable states. Yet, the full potential of these systems, specifically in exploiting parallelism and implementing dynamic scheduling strategies, is largely unexplored. We present MorphStream, a TSPE designed to optimize parallelism and performance for transactional stream processing on multicores. Through a unique three-stage execution paradigm (i.e., planning, scheduling, and execution), MorphStream enables dynamic scheduling and parallel processing in TSPEs. Our experiment showcased MorphStream outperforms current TSPEs across various scenarios and offers support for windowed state transactions and non-deterministic state access, demonstrating its potential for broad applicability.