Running Multiple Craft Sites with Craft Commerce
Craft Commerce does not support running completely independent stores using Craft’s multi-site feature, but Commerce and multi-site can be used together and it’s important to be aware of the limitations.
You could, for example, run a store on two domains like mysite.com and mysite.it and sell products on each one. This would require only one Craft license and one Craft Commerce license.
In this scenario you could add as many sites as you’d like, but there can only be one store.
Orders would appear together in the control panel and store settings like the primary currency, discounts, shipping, etc. would be the same for all sites. (You could still see which site orders originated from even though they’d all appear together.)
Products, however, are multi-site aware similarly to Craft entries. This means content could vary completely for each site, while pricing would still have to be consistent and in the same currency. You could translate content, change which products you choose to display, and change exactly how they’re presented as long as the pricing and currency is not expected to change for each site.
In other words, product information and design emphasis could vary almost without limit for each site—while store configuration and operation would have to be consistent and not site-specific.
If these limitations don’t work for your project, you would need to establish separate Craft installs and license Craft and Commerce for each site separately.
Commerce will eventually have full multi-site support, but there is not yet an ETA. If you’d like to keep an eye on feature development you should consider following these GitHub Issues: