Mapping to different linked servers per database

Question

I have an MSSQL Server 2008 database "DBLive" that link to three different external servers [ExtServer1, ExtServer2, ExtServer3], all defined in sys.servers. There are several stored procedures that refer to stored procs or tables on the external servers, f.x. like 'SELECT TOP 1 @SomeId = Id FROM [ExtServer1].TheExtDB.dbo.SomeTable WHERE ...'.

Here is the challenge - if I want to put an database on the server - "DBTest" which is an identical copy of "DBLive" - but which should connect to different external servers - how do I make [ExtServer1 .. 3] point to a different external servers for "DBLive" and "DBTest"?

If this cannot be done - what would be the preferred way of linking external databases in such a way that two instances of the same db, can have their own external server references - without having differences in the stored procedures?