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Refactoring only goes so far in this case, since we can only realistically refactor one application. Unit tests help the refactored application but they don't guarantee that all of the other pieces (DB stored procs, MS Access, classic ASP, assorted other bits) still work.
I am torn.
We are not really a startup, but we are small and have a startup attitude among the technology people. The platform we are running on goes back about 10 years, and it's starting to show.
There is a single shared database that is used by MS Access, classic ASP, and ASP.NET applications. This means you can't change any one piece without affecting all of the others. We've had people leave because of the resistance to change inherent in the platform. Tiny little changes are very very hard to make sometimes. Small changes can take weeks. Certain major changes might as well be impossible.
But then all of the advice I've ever heard says "don't rewrite." What if we don't rewrite, but build a new platform? Solve different problems than the original?