There's no parameter to enable that. You'd need to modify the invoice address XML file found below.

components/com_comprofiler/plugin/user/plug_cbpaidsubscriptions/xml/edit.front.invoice.xml

You then need to remove the <if node around the VAT input. Example as follows.

FORM:TO:

I fully understand your use-case, but I also believe that this is a seldom use-case up to now, as it is the first time that we have received this request since the first release of CBSubs tax plugin. Maybe things changed and we will see more such requests from Italy and other EU countries ?

Also the equivalent US Social-Security Number or personal tax number in a number of countries is considered as a private number, sometimes even a secret one, like in the US, as it allows to impersonate someone. Thus I am unsure if we will make this a standard feature at this time.

However, Kyle's proposal can be implemented into a tiny specific (custom) CBSubs plugin that you install on your site and to which you give a higher ordering number than CBSubs Tax plugin. That plugin can have that same XML file (but with just that VAT and fiscal number field and the <if> statement to just override that VAT field, as XML files that may override invoice are auto-loaded from CBSubs plugins. That way it's not a hack, and survives upgrades. You would obviously also need to add the corresponding fiscalnumber database column to the cbsubs_paymentbaskets table.