Switching Between Basecamp accounts
As long as you use the same exact email address to access each Basecamp account, you can navigate between them in your browser.* You can see all of the accounts you're a part of here: https://launchpad.37signals.com/signin
Access the Launchpad or your other accounts from within Basecamp 4 by clicking on the Basecamp logo on the upper-left corner of the page:
If you use the Basecamp 4 desktop app or mobile app, you can only navigate between other Basecamp 4 accounts. So, you would not be able to access a Basecamp 2 account from the Basecamp 4 app.
In the desktop app for Mac, click the Account menu then choose the account you're looking for. You can even opt to use a keyboard shortcut like ⌘1 to navigate to other accounts even more quickly: