Thank you janet4now!
But, as I said, Multisite is not an option, because what I need is every "subsite" to share the same information.
Specifically, I'll be using Woocommerce, every "subsite" will be a shop with the same products and, as far as I have been able to try, a multisite WordPress with Woocommerce makes every subsite "independent" from the next, meaning that each one has its own products and clients.
Thats why I think the best approach would be a plugin that maps a few different domains to my WP installation, and displays a different theme according to which domain the user is coming through. Actually, any solution that allows me to share products between Woocommerce installation in my multisite would do (as long as it doesn't require to export-import products and stock to each store every time there is a change).
I found a plugin like that, but, as I said, it is too old and probably outdated. Unfortunately, I couldn't find it again to show it here.
So, anybody can tell me about any plugin or solution to do what I need?