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The bistablity onset due to the interaction of high-to low-frequency oscillations in the Duffing oscillator is considered. It is shown that such interaction results in arising of additional bistable states, which has a lower threshold for bistability with respect to the forcing amplitude as compared to the harmonically forced oscillator. This phenomenon is illustrated by considering two examples, including the oscillator with a tandem low-and high-frequency external forcing, and the harmonically forced oscillator with a modulated natural frequency. It is shown that three frequency resonances are responsible for the arising of the additional bistable states. The corresponding threshold values of the forcing amplitudes are found analytically. A comparative analysis of different types of bistable states in the oscillator is presented as well.