Strategic classification investigates the interaction between a decision-maker (modeled as a jury) and individuals (agents) who may strategically modify their features to obtain favorable outcomes. A key challenge in this setting is strategic improvement, which focuses on designing incentive mechanisms that encourage individuals to improve their true qualifications. In real-world scenarios, decision-making often involves multi-dimensional evaluations composed of multiple sub-indicators and a final comprehensive assessment. However, most existing paradigms for strategic classification rely on a single decision model, which is inadequate for capturing the complexity of such settings. To address this gap, we introduce the problem of Strategic Improvement with Decision Interactions (SIDI), a novel setting that incorporates multiple interacting decision models and an overarching evaluation mechanism. We analyze the influence of decision interactions and reveal how correlations among classifiers can exacerbate manipulative behaviors. Building on these insights, we propose a decorrelation-based strategic improvement framework that leverages decision interactions to promote authentic qualification enhancements. Extensive experiments on both real-world and synthetic datasets demonstrate the effectiveness of our framework in encouraging genuine improvements while maintaining robust accuracy. Our findings highlight the importance of modeling decision interactions and provide new directions for strategic machine learning.