We developed a general theory that allows to predict the power factor n in the asymptotics of the tunneling magnetoresistance (TMR), T M R ∝ N n , in the limit of large number of the tunnel barrier layers, N , for a magnetic tunnel junction (MTJ) system that has the so-called symmetry spin filtering properties. Within this theory the only information required to determine n is the knowledge of the symmetries of the wave functions of the bulk electrode and barrier materials at the Γ-point in the in-plane surface Brillouin zone. In particular, we show that for a MTJ that has the in-plane square symmetry only three values for the power factor are allowed: n = 0, 1, and 2 for the asymptotics of the TMR enhanced due to the symmetry spin filtering mechanism. To verify our theory we performed the Density Functional Theory (DFT) calculations of transmission functions and TMR for Fe/MgO/Fe MTJ which confirm predicted values of the power factor n = 0, 1, or 2 in specific ranges of energies (in particular, n = 1 at the Fermi energy).