Update: Support for Outlook 2003 has been added to ExtraOutlook.
Update: In case the main ExtraOutlook website is down, I uploaded a copy of the program onto this website. A copy of ExtraOutlook 1.2 is available here: ExtraOutlook 1.2
Normally you can only connect to one Exchange server at a time with Outlook. But a recently released 3rd party application name ExtraOutlook will allow you to open more than one instance of Outlook with each instance connected to a different Exchange server. Currently this 3rd party application only works with Outlook 2007 but an Outlook 2003 version is being worked on by the developers. You can download the application from the Hammer of God Website.