Transactional stream processing engines (TSPEs) differ significantly in their designs, but all rely on non-adaptive scheduling strategies for processing concurrent state transactions. Subsequently, none exploit multicore parallelism to its full potential due to complex workload dependencies. This paper introduces MorphStream, which adopts a novel approach by decomposing scheduling strategies into three dimensions, and then strives to make the right decision along each dimension, based on analyzing the decision trade-offs under varying workload characteristics. Compared to the state-of-the-art, MorphStream achieves up to 3.4 times higher throughput and 69.1% lower processing latency for handling real-world use cases with complex and dynamically changing workload dependencies.