Is there a way in SQL Server Management Studio 2005 (or later) to change the Windows Authentication user (as you could in SQL Server 2000 and older)?
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There are many places where someone might want to deploy this kind of scenario, but due to the way integrated authentication works, it is not possible.
As gbn mentioned, integrated authentication uses a special token that corresponds to your Windows identity. There are coding practices called "impersonation" (probably used by the Run As... command) that allow you to effectively perform an activity as another Windows user, but there is not really a way to arbitrarily act as a different user (à la Linux) in Windows applications aside from that.
If you really need to administer multiple servers across several domains, you might consider one of the following:
Hopefully this helps!