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We explore experimentally bichromatic (frequencies and $\omega _2$) photoresistance of a two-dimensional electron system in the regimes of microwave-induced resistance oscillations and zero-resistance states. We find bichromatic resistance to be well described by a superposition of and components, provided that both monochromatic resistances are positive. This relation holds even when the oscillation amplitudes are small and one could expect additive contributions from monochromatic photoresistances. In contrast, whenever a zero-resistance state is formed by one of the frequencies, such superposition relation breaks down and the bichromatic resistance is strongly suppressed.

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