I can't stay logged in to multiple accounts at once. It appears that only the first Basic authentication account can be saved. All subsequent accounts lose their password on quit and relaunch.

1. Launch Sourcetree for the first time and add a Bitbucket Server account with your Personal Access Token.
2. Add a GitHub Enterprise account with your Personal Access Token for that system.
3. Quit and relaunch Sourcetree.
4. Show the remote hosted repositories.

Sourcetree prompts you for the password to the Github Enterprise account. Entering the personal access token doesn't actually work, you have to go into Preferences and enter the password in the account tab, and then re-enter it to verify (I'm not sure why). Then the password sticks until you quit and relaunch again.