In Larry Niven's short story "Bordered in Black", there's a planet (Sirius B-IV) with much lower gravity than Earth. As a result, the planet has a gentler atmospheric pressure gradient, i.e., the air pressure changes less over the same vertical distance. Because of this, the planet had clouds as high as 130 kilometers.
It got me thinking: there's a world I've been building for some time that has an extreme vertical component to its geography, with some features being hundreds (and in one extreme case, thousands) of miles tall. It occurred to me a while ago that air pressure would be a serious problem in this setting, since most of that vertical space, although not necessarily the upper- or lower-most extremes, is meant to be habitable. I initially decided to handwave it away, judging the problem to be insurmountable.
Now Niven has reignited my interest in finding a scientific explanation for this. Using real physics, what are some good explanations for a range of livable air pressure extending over several hundred vertical miles? If this isn't possible, what's the largest vertical distance over which air pressure can remain can livable?
Side note: the ground is made out of handwavium. I am not breaching the topic of how hundred-mile-tall features exist in this world. The air on the other hand, being breathable, is normal nitrogen-oxygen, and thus requires an explanation for its behavior.