You may be misunderstanding what an upgrade is - this seems to be a fairly common misconception.
A major upgrade (RemovePreviousVersions) is not a patch, or hotfix or anything you might think of as updating the files in the currently installed product. A major upgrade is a complete product install of a full working product that happens to include removal of an earlier version if there is one installed. Requirements to perform a major upgrade include having a higher product version and a different product code.
On the other hand if you want to install two "copies" of the same product, then simply don't use a major upgrade, and change your product code (and package code). You'll get two copies of the same product installed, and whether that all works depends among other things on whether the two copies of the application play well together and whether you can uninstall one without damaging the other.