In additive framework you can also handle this with time-varying coefficients on the seasonal components.
I’d say the most “tried and true” approach though is to just apply a data transformation to try to minimize the change in variance over the time series. Usually taking logs is enough (in that case you were in the multiplicative regime that @drbenvincent pointed out). Sometimes you can do something more exotic like box-cox, or Guerreo correction – see here for discussion.
Last comment – changes in variance shouldn’t be a problem for Fourier seasonality, because saturated Fourier basis can conform to any arbitrary function. Is the problem in your forecasts?