While there’s no way to connect to multiple servers as different users in a single instance of SSMS, what you’re looking for is the following RUNAS syntax:
runas /netonly /user:domain\username program.exe
When you use the /netonly
switch, you can log in using remote credentials on a domain that you’re not currently a member of, even if there’s no trust set up. It just tells runas that the credentials will be used for accessing remote resources – the application interacts with the local computer as the currently logged-in user, and interacts with remote computers as the user whose credentials you’ve given.
You’d still have to run multiple instances of SSMS, but at least you could connect as different windows users in each one.
For example: `runas /netonly /user:domain\username ssms.exe`