This note generalizes the results in Li et al. (2012) to threshold moving-average (TMA) models with more than two regimes. Under some mild conditions, it is shown that multiple-regime TMA models are always strictly stationary and ergodic without any restriction on the coefficients. This is very different from threshold AR models. An explicit/closed form of the solution to the multiple-regime TMA model is derived as well. A three-regime TMA model is illustrated with an application to monthly data of the exchange rate of the Japanese yen against the USA dollar from January 1971 to December 2000.