  Improving our understanding of the nuclear properties of high-Eddington ratio
($\lambda_\mathrm{Edd}$) active galactic nuclei (AGN) is necessary since the
bulk of X-ray spectroscopic studies have been focused on low-Eddington AGN. We
present here the X-ray spectral analysis of 14 radio-quiet,
$\lambda_\mathrm{Edd}\gtrsim1$ AGN at $0.4\leq z \leq 0.75$, observed with
XMM-Newton. Optical/UV data from simultaneous Optical Monitor observations have
been also considered. These AGN have been selected to have relatively high
values of black hole mass ($M_\mathrm{BH}\sim10^{8-8.5}M_\odot$) and bolometric
luminosity ($L_\mathrm{bol} \sim 10^{46}$ erg s$^{-1}$), in order to complement
previous studies of high-Eddington AGN at lower $M_\mathrm{BH}$ and
$L_\mathrm{bol}$. We studied the relation between $\lambda_\mathrm{Edd}$ and
other key X-ray spectral parameters, such as the photon index of the power-law
continuum $\Gamma$, the X-ray bolometric correction $k_\mathrm{bol,X}$ and
$\alpha_\mathrm{ox}$. Despite the homogeneous optical and SMBH accretion
properties, the X-ray properties of these high-Eddington AGN are quite
heterogeneous. We measured values of $\Gamma$ comprised between 1.3 and 2.5, at
odds with the expectations based on previously reported
$\Gamma-\lambda_\mathrm{Edd}$ relations, by which $\Gamma\geq2$ would be an
ubiquitous hallmark of AGN with $\lambda_\mathrm{Edd}\sim1$. We found that
$\sim30\%$ of the sources are X-ray weak, with an X-ray emission about a factor
of $\sim10-80$ fainter than that of typical AGN at similar UV luminosities. The
X-ray weakness seems to be intrinsic and not due to intervening obscuration.
This may indicate that high-Eddington 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 AGN suggest that these periods can last for several
years.
