Unlike many other services, the Fastmail web interface has full support for logging in to multiple accounts at the same time. When you go to our homepage, you will be brought to our Switch User page, which shows any accounts you are currently logged in to. Select one to go to the account's Inbox. To log in to another account, click the Log in to another account link at the bottom of the list.
If you check off the Keep me logged in option when you log in, then going to our homepage will take you straight to the Inbox instead of showing currently logged in accounts. To log in to another account in this situation, go to https://login.fastmail.com.