If you had Creative Cloud subscription, you can use cloud storage.
However we can not confirm your mention "save", do you want to backup your site data?
So you can backup your site data to your cloud storage.
If you intend to migrate web hosting service, you can make use Adobe Web Hosting service (aka Business Catalyst).
This service required some fee in addition to CCM subscription if you want to use any additional function like shopping cart, site analytics, marketing mail.