Can you confirm that you have verified your VAT through VIES?
If it is showing as invalid, then you will need to talk to your local tax authority to resolve the issue.
If it is showing as valid in VIES, then please:
Make sure you aren't copying and pasting the number to ensure that there aren't any spaces at the front or the end of the ID.
Make sure your store address is set to the same country as the first two letters of your VAT ID.
If it is still not accepting, please select the option 'I do not have a VAT number' and confirm. Save their settings with no VAT ID and wait 24 hours before trying to add it again. It should be accepted the next time as long as it was removed for 24 hours.
If the VAT is still showing as invalid, then we'll need to reach out to our Tax team for further assistance. While we’re not able to provide account-specific support via the Shopify Community at this time, we’d be happy to continue assisting you through live chat, email, or callback. Please visit https://bit.ly/3cJkx8V and log in to your account to create a support request.
Since this is the next step I've marked this reply as the solution for the benefit of others who may discover this topic. Thanks!
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