How do I invoice an EU customer without valid VAT number?

To enable invoicing to such customers, you should mark these customers in the Partner table as Private Person and leave the VAT number field empty.

Some EU customers do not have a valid VAT number or do have a VAT number which is valid for domestic use only.

In Scope you can mark a EU VAT Number as valid for domestic use only, but during invoicing, when the customer is in a different country, it will block the invoicing and give a validation error on the VAT number.

Master data > Partner > General tab ... Business Type

To enable invoicing to such customers you should mark these customers in the Partner table as Private Person and leave the VAT number field (Registration IDs tab) empty.
This will make that Scope does not print the VAT number on the invoice and VAT is charged and printed.