<p>The present study focuses on the properties of turbulent fluctuations in the solar wind observed during the interplanetary coronal mass ejection (ICME) on 10–11 May 2024. The disturbance caused substantial compression of the magnetosphere and a very intense geomagnetic storm. A set of spacecraft (Wind, THEMIS, MMS, and GOES-18) provided high-resolution measurements of magnetic field parameters, allowing us to analyze the evolution of magnetic field fluctuation properties along the path from L1 to the bow shock and across the bow shock in different regions within the ICME. This study is based on a comparison of simultaneous measurements from pairs of spacecraft. Spectral scaling, the compression coefficient, and the flatness of the probability distribution function were examined in the transition range between the MHD and kinetic regimes. The results demonstrate that during the ICME, spectral scaling is preserved at MHD scales as the plasma propagates from L1 to the bow shock, while the kinetic-scale part of the spectra may change. The properties of intermittency are nearly identical at L1 and closer to the bow shock during disturbed solar wind conditions, although they may vary significantly during steady solar wind. Crossing the bow shock results in substantial spectral modification throughout the dayside magnetosheath and an increased role of compressive fluctuations in the turbulent cascade. The identified turbulence properties and their evolution appear to be typical of ICMEs and do not reflect peculiarities specific to the outstanding 10–11 May 2024 event.</p> Graphical Abstract <p></p>