I think you should try to simplificate the problem. if some elements are required to be present on invoice, it doesn’t mean there are forbidden to be here in others cases.
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print VAT number if you have it on Party (whatever it is required or not). Please note it is still your responsability to have it when it would be required.
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always print mentions whatever the kind of customer
about VAT number to tell if a party is professional or not, it isn’t enough: some professional doesn’t have VAT number because they aren’t “assujettis à la TVA” like “auto-entrepreneurs” (and also professional “au forfait” like farmers). But they are still professionals.