How high can a mountain possibly get?
Found an article that used a simple analytical modelling to determine how high a mountain can be. Reference

Based on simple physics, tallest a mountain will be on Earth is ~10 km.
This is based on:


Simple cone shape for the mountain. Vol ≈ $r^2 h$
Based on weight of the mountain:  Weight W ≈ $\rho g r^2 h$
Stress σ the mountain exerts on the ground underneath it is:

σ ≈ Weight/Area ≈ $(\rho g r^2 h)/r^2$ ≈ $\rho g h$
The limiting factor is the compressive strength of the rock:
Assume granite with an average density $ρ$ = 3 g/cm$^3$.
Compressive strength is $\sigma_C$ = 200 MPa = $2 \times 10^8\, N/m^2$
Stress = Compressive strength of rock  σ = $\sigma_C$ or $\rho g h_{max} = \sigma_C$.
Calculate max height:

$h_{max}$ ≈ $\sigma_C/(\rho g)$

$h_{max}$ ≈ $\frac{2 \times 10^8\, N/m^2}{3 \times 10^3 kg/m^3 \times 10\, m/s^2)}$≈ $10^4\, m$ = 10 km