This paper presents a numerical study of the linear and non-linear stability of thermosolutal convection within a porous medium saturated by a non-Newtonian binary fluid. The power-law model is utilized for modeling the behavior of the working medium. The given statement implies that the horizontal boundaries experience thermal and solutal flow rates, whereas the vertical walls are impermeable and thermally isolated. The relevant factors that govern the problem being investigated are the Rayleigh number, , the power-law index, , the cavity aspect ratio, , the Lewis number, , and the buoyancy ratio, . An analytical solution is obtained for shallow enclosures ( ) using the parallel flow approximation and a modified form of the Darcy equation. By solving the entire set of governing equations, a numerical investigation of the same phenomenon was conducted. One of the most intriguing discoveries from this research is that it identifies a bi-stability phenomenon, this particular phenomenon signifies the existence of two stable solutions. The results obtained from both methods demonstrate a good level of agreement across a diverse range of these governing parameters.