Existing power and design methods for multiple-intervention stepped wedge designs (M-SWDs) typically assume exchangeable cluster-period correlation, despite evidence that correlation often decays over time. Misspecification of this correlation structure can substantially distort variance estimation and power, particularly for treatment interaction effects. We develop a unified covariance framework for M-SWDs that separates intracluster correlation from an explicit cluster-period correlation matrix. This formulation accommodates exchangeable, autoregressive, and more general distance-dependent correlation structures while preserving closed-form expressions for the variance of treatment effect estimators under linear mixed models. Using analytic results and simulation studies, we demonstrate that assuming uniform correlation when the true structure is time-dependent can lead to substantial power mischaracterization. Specifically, we find that designs calibrated under independence assumptions may be overly conservative and compound symmetry can be either optimistic or conservative. These findings demonstrate the importance of explicitly modeling cluster-period correlation at the design stage of M-SWDs and provide practical guidance for power calculation and design selection in realistic settings.

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