We can calculate the maximum possible height of the mountain on earth. If the elastic limit of a typical rock is $3 \times 10^8\ \mathrm{N/m}$ and its mean density is $3 \times 10^3\ \mathrm{kg/m^3}$, then the breaking stress is $h\,\rho\,\mathrm{g}$, where $h$ is height, $\rho$ is the density of the rock, and $\mathrm{g}$ is the acceleration due to gravity. Then
$$ h = \frac{\mathrm{elastic\ limit}}{\rho\,\mathrm{g}} $$
Putting the values we get,
$$ h = 10^4\ \mathrm{m} $$
which is the maximum possible height. Now Mount Everest is within this limit, but Mauna Kea is 10,210 m tall (measured from its oceanic base).
Does this suggest that rock types at the base of this mountain are different? Or does the presence of water have an effect?