Even though chrome runs tabs as different processes it appears to not support this... any ideas or documentation I might have missed?
Try two different incognito windows.
If you want to stay logged in for a period of time, the best thing to do is to create a new profile for each set of credentials. Click the face icon in the top right-hand corner and select "new user."

If you just want to log-in with different credentials once, it might be easier to use incognito mode, as rmmh said.
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