Boiling with the lid partly on does not itself reduce the amount of steam; but it means you need slightly less power to maintain the boil, and that does.
If your extractor can’t keep up then you might like to look at the steam condenser setup that @chopps has done on his larger scale setup… essentially a cover that routes the steam into a downwards pipe with a bit of cold water spraying into it. The spray condenses the steam and it just drips into a bucket. Very neat.
It’s mentioned in this episode of his brewery build video (which is very much worth watching in its own right):
Wow very interesting video and will be watching more in the series. thanks TETB