In Larry Niven's Known Space books, the planet Plateau is about 80% the size of Earth, and is dominated by a thick, opaque, unbreathable atmosphere. Except that it is breathable at an altitude of 40 miles. Conveniently (or otherwise) there is a mountain that rises to this height, with a plateau about "half the size of California", known as Mt Lookithat. This plateau has been colonised.
Now, the meme has been going about the internet that a mountain that high is flat out impossible. I looked into it and found this article, How high can a mountain be? (J. Astrophys. Astr. (1981) 2, 165–169):
In a homogeneous rock stable mountains cannot rise much further than h1 = Y/ρg above the level of the surrounding plains. Gently sloping ‘hills’ of crustal rock, ‘floating’ in more or less isostatic conditions on denser material, may be able to rise to greater heights of the order of h2 = (h1 b)0.5 where b is the base of the ‘ hill ’.
(Where Y is Young's Modulus for the material, ρ is the density and g is the local gravity.)
For granite on Earth, Y is 1·5 × 106 kg m–2, and ρ is 2·65 × 103kgm–3, and you get h1 equal to 2250m. Assuming a uniform slope and homogenous material and a base of around 1000km across, then h2 comes to roughly 45km. Note that the Himalayan plateau is roughly 1000km across, and reaches roughly four times h1 (Everest is 8.8km).
Plugging in the numbers for Plateau, we get h1 = 2780 km and h2 = 53 km (or 33 miles).
So, theoretically, it is not outside the bounds of possibility for Mt Lookithat to be not far off the stated height. Things that can be done to increase the theoretical height (and 4h) might include using a lighter, stronger material than Earth-normal granite, giving the mountain a wider base, having it 'float' on a denser material than on Earth, and having an unusually uniform structure. Note that Mauna Kea actually rises higher than Everest when measured from the ocean floor (10.2km), and has a base of around 150–200km across.
Mt Lookithat is meant to be unusual, and you have to play with the numbers and the assumptions to make it so, but I don't think that we know enough about xeno-geology to state definitively that it's flat out impossible.
A more serious question to me has always been, just what makes the oxygen that the colonists breathe?
Current Music: Ain't No Mountain High Enough—Diana Ross & The Supremes