Aims: Flip-flops are top-hat-like X-ray flux variations which occur in some transient accreting black hole binary systems and feature simultaneous changes in the spectral hardness and the Power Density Spectrum (PDS). They occur at a crucial time in the evolution of these systems, when the accretion disk emission starts to dominate over coronal emission. Flip-flops have only rarely been observed and are poorly understood. Methods: We detect 15 flip-flops in the 2018 outburst of Swift J1658.2-4242, in observations by XMM-Newton, NuSTAR, Astrosat, Swift, Insight-HXMT, INTEGRAL, and ATCA. We analyse their light curves, search for periodicities, compute their PDS, and fit their X-ray spectra, to investigate the source behaviour during flip-flop transitions, and how the interval featuring flip-flops differs from the rest of the outburst. Results: The flip-flops of Swift J1658.2-4242 are of an extreme variety, exhibiting flux differences of up to 77% within ~100s, much larger than has been seen so far. We observe radical changes in the PDS simultaneous with the sharp flux variations, featuring transitions between the Quasi-Periodic Oscillation types C and A, which have never been observed before. Changes to the PDS are delayed, but more rapid than changes in the light curve. Flip-flops occur in two intervals, separated by two weeks in which these phenomena were not seen. Transitions between the two flip-flop states occurred at random integer multiples of a fundamental period, of 2.761ks in the first interval, and 2.61ks in the second. Spectral analysis reveals the high and low flux flip-flop states to be similar, but distinct from intervals lacking flip-flops. A change in the inner temperature of the accretion disk is responsible for most of the flux difference in the flip-flops. We highlight the importance of correcting for the influence of the dust scattering halo on the X-ray spectra.
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