With a relay.
Yeah, I was afraid you'd ask me that. . .
From 11.5 to 12 you need series closed relay contacts.
From 12 + and above you need open relay contacts and a low drop regulator in parallel with the relay contacts, so the relay contacts would need to be driven by a voltage sensing comparator.
But, I don't know what to do with the region between 12.000 v and when the low drop out regulator kicks in. Not to sound like Bill Clinton, but it depends on what you mean by "same."
If the input voltage varies you could bridge the gap with a large capacitor. In that case, maybe you could intentionally dither the input voltage above and below the questionable region, but that would also make the relay oscillate.
I have to sleep on this one.