We propose a locally stationary seasonal AR process allowing for multiple periodicities and separate time-varying parameter processes in both the regular and seasonal parameters. Both the regular and seasonal parameters are parameterized to guarantee stationarity at every time point. The time evolution is modeled by dynamic shrinkage processes to allow for both longer periods without change and rapid jumps. A Gibbs sampler is developed with a particle Gibbs update step for the parameter trajectories. The model and the numerical effectiveness of the Gibbs sampler is investigated on simulate and real data.