I would go back to basic first, why do you need a more powerful fan? My shower room the extractor has failed, and since we have no problems done nothing to correct it.
I have looked at three houses and their shower rooms, two no problem, one mould growth, and it is nothing to do with the bad house being just outside Mold.
It is all down to the chimney effect. The house with the problem the shower is over the bath, so the shower doors can't seal either top or bottom, and the floor is not tanked, so it needs doors around the shower, so air goes in below the door over bath, and out above it meaning the whole room gets damp.
The other two houses, one was a wet room so no doors or curtain around the shower, the other the doors seal at the bottom, so in both cases no chimney effect, all water retained local to shower. Whole room does not get wet.
The other problem is where and when the air is drawn from the shower, with the vent above the shower again stops air circulating around the room, however it can be darn cold, so really want the extractor to run when we have finished showering not while having a shower, and the replacement air needs to come from some where dry.
This house humidity is around the 50% in fact 38% today, the house with a problem, rare would see humidity under 70% not talking about the shower, but the rooms the shower extractor is dragging the replacement air from. The shower room needs to be hotter than the room taking the replacement air from. Best is get replacement air from outside.
My first house was very dry, has gas hot air central heating, and would place trays of water in the air intake to try and make house damper, plants are good at lifting the humidity, or bad at getting humidity too high if house already too humid. Windows are a big problem, we would have metal frames for the windows and a catchment tray to lead the condensate outside with the old single glazed windows, as double glazing came in we also got central heating, so ventilation and moisture did not go through the roof as with solid fuel heating, but the moisture was allowed to build up, today vents are built into windows, but early double glazing tried to seal the house.
