I would like to open a new MonoDevelop instance to work on a different project on the Mac, and the OS is currently preventing me from opening a new instance.
On Mac, if you have an app open and you try to launch it again, the Mac just switches to the open app. You can force it to open a new instance by passing the option "-n" to the launcher. In a terminal, run
open -n /Applications/MonoDevelop.app
Note also that MonoDevelop is capable of opening multiple solutions. To do this, simply uncheck the "close current solution" checkbox in the "Open" dialog, or hold down the control key when clicking on one of the recently opened projects in the Welcome Page.
EDIT: For Xamarin Studio, which has replaced MonoDevelop on Mac, the command is
open -n /Applications/Xamarin\ Studio.app
EDIT 2:
For Visual Studio for Mac, which has replaced Xamarin Studio, the command is
open -n /Applications/Visual\ Studio.app