We present the results from an X-ray and optical study of a new sample of eight extreme luminosity ultraluminous X-ray source (ULX) candidates, which were selected as the brightest ULXs (with LX > 5 × 1040 erg s−1) located within 100 Mpc identified in a cross-correlation of the 2XMM-DR1 and RC3 catalogues. These objects are so luminous that they are difficult to describe with current models of super-Eddington accretion on to all but the most massive stellar remnants; hence they are amongst the most plausible candidates to host larger, intermediate-mass black holes (IMBHs). Two objects are luminous enough in at least one observation to be classed as hyperluminous X-ray source (HLX) candidates, including one persistent HLX in an S0 galaxy that (at 3 × 1041 erg s−1) is the second most luminous HLX yet detected. The remaining seven sources are located in spiral galaxies, and several appear to be closely associated with regions of star formation as is common for many less luminous ULXs. However, the X-ray characteristics of these extreme ULXs appear to diverge from the less luminous objects. They are typically harder, possessing absorbed power-law continuum spectra with Γ∼ 1.7, and are potentially more variable on short time-scales, with data consistent with ∼10–20 per cent rms variability on time-scales of 0.2–2 ks (albeit at low to moderate significance in many data sets). These properties appear consistent with the sub-Eddington hard state, which given the observed luminosities of these objects suggests the presence of IMBHs with masses in the range of . As such, this strengthens the case for these brightest ULXs as good candidates for the eventual conclusive detection of the highly elusive IMBHs in the present-day Universe. However, we caution that a combination of the highest plausible super-Eddington accretion rates and the largest permitted stellar black hole remnants cannot be ruled out without future, improved observations.