I am looking for a solution for when a foreign (within EU) company orders from us. I should then not charge VAT, but Shopify does not provide this possibility (or I am missing something). Is there anyone who also has experience with this and knows a solution?
Shopify is mostly for B2C unless you go for Shpofy + (and one probably would not unless one has extra 2000 USD per month). So you are stuck with B2C and automatic tax collection unless you set tax exemption on the customer (works on only on VAT exclusive setting!!!!!!)
So if a registered customer comes with their email they will be exempted from taxes.
You can also try B2B apps (there are many) but they use more or less the same principle.
Alternatively, you can always create a draft order with no taxes in.