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SARIMA models and exponential smoothing methods are classical approaches to account seasonal dynamics. However, they tipically allow to model just one periodic component, while many empirical time series data show multiple seasonality, possibly interlacing toghether. To face this case, different decomposition models have been proposed in literature, while SARIMA models have been quite neglected. To fill the gap, in this work we suggest a suitable specification of the SARIMA model able to account multiple seasonality. We call it mSARIMA. To study the performance of this class of models, we compare it with two popular seasonal-trend decomposition approaches, namely the TBATS and MSTL models. A simulation exercise shows that mSARIMA models are more effective in describing the the different seasonal components.