.NET migrations: Setup and migrate multiple databases at runtime

Brief introduction:
I have this ASP.NET Webforms site with the particularity that it doesn’t have only 1 database, it has many.
Why? Because you can create new “instances” of the site on-the-fly. Every “instance” share the same codebase, but has its own database. These all databases have the same schema (structure) but of course different data. Don’t ask ‘why don’t you put everything in one database and use InstanceId to know which is” because it’s a business policy thing.