I've yet to see a large system with lots of subsystems rewritten in one go, but I'm more than open to being convinced that it can be done so if you could please do a write-up of how such a project was managed.
The ones I have seen - and this is actually one of the major reasons the clean-up crew gets called in the first place - is big bang rewrite projects gone astray.
One huge problem with rewrites of old code is that the requirements are no longer known or even misunderstood.
The biggest problem with "the new system" is that it's rarely a rewrite of the second system. Obviously someone liked the old system otherwise it wouldn't be rewritten. But the business case for the new system isn't just lower maintenance cost, higher performance, a modern look etc. It's always going to be all those new features. That's what sinks the new project.
The ones I have seen - and this is actually one of the major reasons the clean-up crew gets called in the first place - is big bang rewrite projects gone astray.
One huge problem with rewrites of old code is that the requirements are no longer known or even misunderstood.