In QuarkXPress for Mac OS, you can switch between open projects using a system-level shortcut. In order for this shortcut to work, though, it must be turned on in System Preferences. To make sure this shortcut is turned on, launch System Preferences, click Keyboard & Mouse, display the Keyboard Shortcuts tab, and make sure Move focus to next window in active application is checked. This shortcut is turned on by default. To cycle through project windows the keyboard command is Command~.
In QuarkXPress for Windows, you can switch between open project using the keyboard command of ControlTab. This keyboard command is turned on by default.