To sign out of the Xbox App on Windows 10, go to Settings, select the General tab, and immediately under this should be a Sign out option. Click this and the Xbox App will sign out and you will be at a green
screen with the option to Sign in. If you click Sign In it will start to sign in as the original account, but there will be an option on the next screen stating Sign in with a different Microsoft account.
Click this and you can sign in as a different MS account for the Xbox app while still logged in to Windows under the original MS account.
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