EU VAT Number for WooCommerce

The VAT in Switzerland works pretty much the same as in the EU. Except for the authorities in charge.

The Swiss government offers a service similar to the one you use to validate/verify EU VAT numbers. You can find the documentation here: https://www.bfs.admin.ch/bfs/en/home/registers/enterprise-register/enterprise-identification/uid-register/uid-interfaces.html

So it seems that it should be possible to extend your extension with Switzerland with the same functionality as you offer for the other European countries.