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We study the impact of saturable nonlinearity on the presence and location of exceptional points in a non-Hermitian dimer system. The inclusion of the saturable nonlinearity leads to the emergence of multiple eigenvalues, exceeding the typical two found in the linear counterpart. To identify the exceptional points, we calculate the nonlinear eigenvalues both from a polynomial equation for the defined population imbalance and through a fully numerical method. Our results reveal that exceptional points can be precisely located by adjusting the non-equal saturable nonlinearities in the detuning space.