Hello Juan Manuel -
Since your data is on daily frequency, seasonality=7 seems to be the right choice.
Of course this does not address your question about modeling the second seasonality you have discovered in your data.
I certainly understand your concern about proprietary data, but without seeing the data my advise has to stick to conceptual ideas only.
When you say that "there is an almost clockwork-like increase of values from the previous years.", would you describe this pattern as a monthly cycle or a weekly cycle - or do you see level shifts across several years?
What I'm getting at is the fact the you should be able to define either discrete events such as calendar events Jan-Dec or Week1-Week52 to model this effect. Alternatively you may want to introduce an adjustment variable which mimics the level shifts. Yet another approach might be to model your data in a 2 step manner: model on daily frequency, model on monthly frequency, and then reconcile both forecasts using the HPFTEMPRECONCILE procedure.
Hope this is useful.
Thanks,
Udo