Context. Flares are powerful events ignited by a sudden release of magnetic energy which triggers a cascade of interconnected phenomena, each resulting in emission in different electromagnetic bands. In fact, in the Sun flares are observed across the whole electromagnetic spectrum. Multi-band observations of stellar flares are instead rare. This limits our ability to extend what we learn from solar flares to the case of flares occurring in stars with different properties. Aims. With the aim of studying flares in the 125-Myr-old stars in the Pleiades observed simultaneously in optical and X-ray light, we obtained new XMM-Newton observations of this cluster during the observations of Kepler K2 Campaign 4. The objective of this paper is to characterize the most powerful flares observed in both bands and to constrain the energy released in the optical and X-ray, the geometry of the loops, and their time evolution. We also aim to compare our results to existing studies of flares occurring in the Sun and stars at different ages. Methods. We selected bright X-ray/optical flares that occurred in 12 known members of the Pleiades from their K2 and XMM-Newton light curves. The sample includes ten K-M stars, one F9 star, and one G8 star. Flare average properties were obtained from integrated analysis of the light curves during the flares. The time evolution of the plasma in the magnetic loops is constrained with time-resolved X-ray spectral analysis. Results. Most of the flares studied in this work emitted more energy in optical than in X-rays, as in most solar flares, even if the Pleiades flares output a larger fraction of their total energy in X-rays than typical solar flares do. Additionally, the energy budget in the two bands is weakly correlated. We also found comparable flare duration in optical and X-rays and observed that rapidly rotating stars (e.g., with rotation period shorter than 0.5 days) preferentially host short flares. We estimated the slope of the cooling path of the flares in the log(EM)-vs.-log(T) plane. The values we obtained are affected by large uncertainties, but their nominal values suggest that the flares analyzed in this paper are mainly due to single loops with no sustained heating occurring during the cooling phase. We also observed and analyzed oscillations with a period of 500 s during one of the flares. Conclusions. The flares observed in the Pleiades can be classified as “superflares” based on their energy budget in the optical, and share some of the properties of the flares observed in the Sun, despite being more energetic. For instance, as in most solar flares, more energy is typically released in the optical than in X-rays and the duration of the flares in the two bands is correlated. We have attempted a comparison between the X-ray flares observed in the Pleiades and those observed in clusters with different ages, but to firmly address any evolutionary pattern of flare characteristics, similar and uniform multi-wavelength analyses on more complete samples are necessary.