I work with a code base that is over 500K lines of code. It is in serious need of refactoring. There have been refactoring efforts identified that will take longer than the normal two week sprint. These can't be broken up into smaller tasks as I have seen suggested in other answers on this site. The product needs to work at the end of the iteration, and partial refactoring will leave the system in an unusable state as the dependency between items is horrible. So what would be the best way to approach this hurdle? Again I mention, breaking it down into smaller pieces is is not an option, that has already been done.

Update: People seem to need an explanation of why this can't be fit into a 2 week sprint. There is more involved in a sprint than just writing code. We have a policy of no code without tests. That policy did not always exist and a large portion of the codebase does not have them. Also some of our integration tests are still manual tests. The issue is not that the refactoring itself is so large. It is with the fact that small changes have an effect on many parts of the system, and we need to ensure that those parts still operate correctly.

We can't put off or extend a sprint because we have monthly hotfixes. So this change extending past a sprint cannot stop the other work being added to the hotfix.