One standard way of modeling and forecasting time series with multiple seasonalities is the TBATS model (De Livera, Hyndman & Snyder, 2011, JASA). It is implemented in the tbats() function in the forecast package for R. See the related tag. More info can be found in section 11.1 of Forecasting: Principles and Practice (2nd ed.) by Athanasopoulos & Hyndman.