The WooCommerce Stock Synchronization plugin allows you to keep the stock quantity of products (based on SKU) in sync across multiple WooCommerce stores. As soon as the stock quantity of a product changes, the plugin will push the new stock quantity to all connected shops. It’s really like magic and works great with both regular WordPress installations as well as multisites.
WooCommerce product stock quantity sync for multisite or any domain
The shops are linked to each other by URL in the plugin settings, so you can sync with WooCommerce running on any of your domains.