In theory you can always have taller mountains if you just have a (exponentially!) wider base. But given all sorts of practical constraints, Earth mountains are pretty much limited to <10 km.

Mostly true on Earth, but not on other planets with lower gravity, and AFAIK it depends on the rock type. Hence why you have Olympus Mons on Mars (or insanely tall ice mountains on Pluto, when that material couldn't form such a steep talus angle on Earth).