I think you have this slightly wrong. It doesn't come with a local database, it comes with a built in GUI to access SQL Server (what ever version). You can use any database you like (multiple databases) and connect to the SQL Server using the Visual Studio version of SSMS.
So, yes, you can install multiple versions of SQL Server on your machine. I currently have 2005 express, 2008 developer edition, 2012 developer edition and express.