I have created a SQL server project in Visual Studio 2015. We have a linked server which is referring to multiple databases. I am unable to find a way to manage this linked server and its references to multiple databases. I am unable to build the solution due to this.
There is no separate type of object on SSDT for linked servers as references. Instead, you should add database reference(s) for your remote database(s) specifying their location as "Different database, different server". Here this process is described in more detail.
You should be able to use the same SQLCMD variable as a server name for all your remote databases, though I haven't tried that myself.