I don't know how interested you are in serving B2B customers in the EU, but at some point, you should add business customer fields at the checkout.
That means, "Business name" and "EU VAT registry number" fields. Using those fields, VAT registered businesses could buy VAT-free from another EU country.
Your system would have to verify the VAT number from the EU VAT registry, which is probably quite a straight-forward process as it seems to be a default function in typical e-commerce software.
Thanks! Someday, hopefully!