Deploying learned decision-making systems often requires transferring to new sites where the sensing pipeline differs. In such cases, observations can change in semantics and dimensionality even when action primitives and objectives remain comparable. In this work, we study transferable model-based planning under this observation mismatch, which remains challenging for existing learning-based approaches. We propose Adaptive Modularized Model (AMM), a modular planning architecture that separates a domain-specific observation adapter from a shared internal dynamics model defined in a common planning state space. The dynamics model is meta-learned from multiple source domains to enable fast adaptation with limited target interaction. At run time, AMM performs receding-horizon planning by rolling out candidate action sequences under the learned dynamics and selecting actions that optimize a task-specific objective over predicted futures. We instantiate the approach on cross-domain traffic signal control, where actions correspond to signal phases and the planning objective captures congestion. Experiments show that AMM improves both performance and data efficiency compared with existing conventional controllers and learning-based baselines.