Mountain bases can support a lot. Everest is not terribly tall from its base, true, but Denali is 5500 meters from base to top and Mauna Kea rises to 10000 meters over base.
Its also a bit of an incorrect picure to think of the interior magma as a liquid. It can flow, but it can also sieze up or crack. Its an in-between, like corn starch and water.