99,9% of companies there are will most likely not have a more than single VAT ID that is relevant to a specific business partner. Granted the fact that a company, let's say is based in country A and sells EU-wide. At some point you may (have to) apply for a VAT ID in these other countries then too, yes. But, your customer is still located in either of these countries - you're not invoicing to multiple companies/countries within the same invoice. That being said, Odoo expects you to, if you have business relationships with a company operating in multiple countries, you still need to be clear about who is the recipient of goods/services and who's the recipient of the invoice. While doing this with a single contact (in the meaning of a res.partner record either of type Company or Individual) it is probably becoming a UX mess.

Hence, Odoo must have decided in the past that a single contact has a single VAT ID. Ultimately another VAT ID should almost always mean a different address as well.*

However, from your point of view - you as a company selling abroad - this isn't even applicable. If you yourself (your company) have multiple VAT IDs, one per country your selling to, Odoo covers this within the functionality of Fiscal Positions (Accounting -> Configuration -> Fiscal Positions using the field Foreign Tax ID).

*) In a multi-company setup (in the sense of multiple res.company records, i.e. your companies) this may actually be an issue if you mean to share contacts across these companies because the VAT ID on that contact is not specific to a company (in this case you should bind the contact to a specific company, set the correct VAT ID (for the first company), duplicate it for the other company and set the relevant VAT ID for this relationship).