[dragonwriter]

> You build the new one whilst the old one is in maintenance mode and swap in new bits as and when you can.

Continuous incremental improvement of a production system may, over time, have the same net effect as a an idealized big-bang replacement, but it's a very different process (it's usually what people who are saying you should never do a ground-up replacement prefer instead, because actual big-bang replacements, unlike idealized ones, are usually a shitstorm: and the reason is that they are usually done to the kind of systems you describe, overcomplicated key systems with inadequate documentation or institutional memory, and they are done instead of trying to get a firm grasp on each component of the existing system before replacing that component. And so they end up, at best, being exceedingly well designed, but overlooking key elements of business function discovered and implemented, but not durably documented, in the original system.)