There used to be a "Multiple IE" installer that would hack things on Windows XP to allow multiple versions of IE to coexist. It has been discontinued for a while, as the page notes:
Multiple IE is no longer maintained and there are no plans to continue maintaining it!
The tactic also apparently resulted in random IE crashes, only worked on Windows XP, and was broken (at least once) by a Windows update.
Instead of trying to hack together a similar solution (which appears to be quite brittle, and will likely be a pain to keep patched with the latest security fixes), it might be easier to consider a completely different approach to the problem:
Fix the Cause:
- Fix/upgrade the underlying legacy code. You may gain compatibility with other, more recent, standards-based browsers as a nice bonus. (Admittedly, this is sometimes not a possible approach.)
Control the Environment:
- Set up a virtual machine running Windows XP with IE6. With a VM, you can ensure the required environment in a stable, tested configuration. There are deployment/integration tools that might be useful as well (users don't necessarily have to know that the app is running in a completely separate instance of Windows XP).
Go Crazy, but (Slightly More) Maintainable*:
- If you can't fix the underlying legacy stuff, it probably isn't being changed much either. Figure out how to actually fix it, and patch it "on-the-fly" to ensure IE7/IE8 compatibility. (i.e. Edit the scripts/CSS/page content/formatting/etc. to resolve issues after it's downloaded, but before the browser engine renders it.)
*(Than trying to get multiple versions of IE working together.)
Those are just ideas, but hopefully they help inspire something useful. Good luck.