We would not recommend filtering it again as there would be a notable reduction in flavour.
The carbon filter will strip a lot of the flavours away from the finished spirit.
You should make sure that you;
- First, complete a stripping run
- Then dilute the collected spirit to 50% or below
- Put this through your filter
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Then dilute the spirit to 20% ABV, and run through the still without saddles and with the botanical basket. This will ensure you have a clean spirit but still hold on to the flavours that you have just added to it.
We advise you to ensure you have the cleanest spirit base when creating the gin/flavoured spirit.