John -
My experience with ISE 3.03 indicates that it uses Windows Installer. Using this version, I was also not able to install the same application twice on the same machine. I discovered that this is the result of a feature called "application self-repair". I also found a way around it.
In the General Information section of the ISE wizard, the last item is Product Code, a GUID that is generated automatically. It is not recommended that you change this code after distributing your product, because users won't be able to re-run the installation for the purpose of repairing files that have been damaged. As you have found out, it also prevents them from re-installing for the purpose of simply putting another copy on their machine.
I found two ways around this: (1) I can create a second installation package identical to the first with the exception of the Product Code. (I just ignore the recommendation and click on "Generate GUID".) or (2) I can add a Feature, perhaps called "Test Copy", that includes the same files as the "Always Install" Feature. If every user doesn't necessarily want test files, I make this Feature optional. I give it a separate shortcut and a separate default folder.