Each webmail instance is on it's own so you can only be signed into one email address within webmail at a time. If you have multiple email addresses with us, you will need to log out before you can log back in with a different email.
If you like using webmail and have more than one email, a way around this is to use a private tab to sign in to the second one or in Firefox, there's a neat thing they offer called "container tabs" and you can assign container tabs to different email addresses so you can have them all open in their own tabs at the same time. You can find out more about those here: https://support.mozilla.org/en-US/kb/containers
If you don't need to use webmail to check your email addresses, you can have multiple accounts set up at the same time in programs like Outlook or Thunderbird or within apps on your devices such as Mail on iOS.