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https://support.steampowered.com/kb_article.php?ref=8625-wrah-9030#share
What you do is sign out on Steam guard app, then set up the 2FA for your other account, once done, do it again for your 3rd account. You will now have an arrow you can press to swap between your 2FA codes for each of the accounts, and just remember which order you set them up, so you use the right code for the right account.
Here an example.
Thanks for you response!