ABSTRACT Most isolated neutron stars have been discovered thanks to the detection of their pulsed non-thermal emission, at wavelengths spanning from radio to gamma-rays. However, if the beamed non-thermal radiation does not intercept our line of sight or it is too faint or absent, isolated neutron stars can also be detected through their thermal emission, which peaks in the soft X-ray band and is emitted nearly isotropically. In the past 30 yr, several thermally emitting isolated neutron stars have been discovered thanks to X-ray all-sky surveys, observations targeted at the centre of supernova remnants, or as serendipitous X-ray sources. Distinctive properties of these relatively rare X-ray sources are very soft spectra and high ratios of X-ray to optical flux. The recently released 4XMM-DR10 catalogue contains more than half a million X-ray sources detected with the XMM–Newton telescope in the 0.2–10 keV range in observations carried out from 2000 to 2019. Based on a study of the spectral properties of these sources and on cross-correlations with catalogues of possible counterparts, we have carried out a search of isolated neutron stars, finding four potential candidates. The spectral and long-term variability analysis of these candidates, using Chandra and Swift-XRT data, allowed us to point out the most interesting sources deserving further multiwavelength investigations.