I was recently working for a client with complex network and a number of security restrictions. I actually had two Active Directory accounts with the client: domain1\jsvoboda and domain2\jim.svoboda.
Most of my work required me to RDP into a machine and connect to databases as domain1\jsvoboda. However on occasion I needed to connect to a different database which required me to connect as domain2\jim.svoboda.
This caused issues, because when using Windows Authentication with SSMS, it passes the credentials of the account you are logged in as.
I could have disconnected from RDP as domain1\jsvoboda and reconnected as domain2\jim.svoboda, however I wanted to find a less time consuming method.
The solution is to open Powershell and run a command like this:
runas /netonly /user:domain\jim.svoboda "C:\Program Files (x86)\Microsoft SQL Server Management Studio 18\Common7\IDE\ssms.exe"
where the value after /user: is the alternate domain account you want to use.
You will be prompted for the password for the alternate domain account, and upon successful entry, SMSS will be started using the alternate credentials.