Hardness-luminosity diagram (HLD) of the sample of HLX candidates considered in this work. Blue filled dots are for sources with a robust association to the host galaxy and empty orange dots for weak associations. The red vertical area indicates the position on the HLD of a typical AGN, with a power law index between 1.8 and 2 (fluxes computed with WebPIMMS; see https://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3pimms/w3pimms.pl). The grey dashed area correspond to the parameter space covered in Gúrpide et al. (2021). The dotted line indicates the conventional HLX luminosity threshold of 1 × 10⁴¹ erg s⁻¹. The long-term spectral evolution of ESO 243–49 HLX-1 is shown in red squares and arrows. The four most interesting candidates analysed in this work (cf. Sect. 5) are marked with red circles and numbered. For those with available data, the long-term evolution or the HR range is reported with grey data points and arrows.