A new flexible tensor-on-tenor regression model that accounts for latent regime changes is proposed. The coefficients are driven by a common hidden Markov process that addresses structural breaks to enhance the model flexibility and preserve parsimony.Anewsoft PARAFAC hierarchical prior is introduced to achieve dimensionality reduction while preserving the structural information of the covariate tensor. The proposed prior includes a new multi-way shrinking effect to address over-parametrization issues while preserving interpretability and model tractability. An efficient MCMC algorithm is introduced based on random scan Gibbs and back-fitting strategy. The model framework’s effectiveness is illustrated using financial and commodity market volatility data. The proposed model exhibits superior performance compared to the current benchmark, Lasso regression.