Improving our understanding of the nuclear properties of high-Eddington ratio (λ Edd ) active galactic nuclei (AGN) is necessary since at this regime the radiation pressure is expected to affect the structure and efficiency of the accretion disc-corona system. This may cause departures from the typical nuclear properties of low-λ Edd AGN, which have been largely studied so far. We present here the X-ray spectral analysis of 14 radio-quiet, λ Edd 1 AGN at 0.4 ≤ z ≤ 0.75, observed with XMM-Newton. Optical/UV data from simultaneous Optical Monitor observations have been also considered. These quasars have been selected to have relatively high values of black hole mass (M BH ∼ 10 8−8.5 M ) and bolometric luminosity (L bol ∼ 10 46 erg s −1 ), in order to complement previous studies of high-λ Edd AGN at lower M BH and L bol . We studied the relation between λ Edd and other key X-ray spectral parameters, such as the photon index (Γ) of the power-law continuum, the X-ray bolometric correction k bol,X and the optical/UV-to-X-ray spectral index α ox . Our analysis reveals that, despite the homogeneous optical and SMBH accretion properties, the X-ray properties of these high-λ Edd AGN are quite heterogeneous. We indeed measured values of Γ comprised between 1.3 and 2.5, at odds with the expectations based on previously reported Γ − λ Edd relations, by which Γ ≥ 2 would be an ubiquitous hallmark of AGN with λ Edd ∼ 1. Interestingly, we found that ∼ 30% of the sources are X-ray weak, with an X-ray emission about a factor of ∼ 10 − 80 fainter than that of typical AGN at similar UV luminosities. The X-ray weakness seems to be intrinsic and not due to the presence of absorption along the line of sight to the nucleus. This result may indicate that high-λ Edd AGN commonly undergo periods of intrinsic X-ray weakness. Furthermore, results from a follow-up monitoring with Swift of one of these X-ray weak sources suggest that these periods can last for several years.