  In this work, which is a continuation of Castell\'o-Mor et al. (2016), we
present new X-ray and infrared (IR) data for a sample of active galactic nuclei
(AGN) covering a wide range in Eddington ratio over a small luminosity range.
In particular, we rigorously explore the dependence of the optical-to-X-ray
spectral index $\alpha_{OX}$ and the IR-to-optical spectral index on the
dimensionless accretion rate, $\dot{\mathcal{M}}=\dot{m}/\eta$ where
$\dot{m}=L_{AGN}/L_{Edd}$ and $\eta$ is the mass-to-radiation conversion
efficiency, in low and high accretion rate sources. We find that the SED of the
faster accreting sources are surprisingly similar to those from the comparison
sample of sources with lower accretion rate. In particular: i) the
optical-to-UV AGN SED of slow and fast accreting AGN can be fitted with thin AD
models. ii) The value of $\alpha_{OX}$ is very similar in slow and fast
accreting systems up to a dimensionless accretion rate
$\dot{\mathcal{M}}_{c}\sim$10. We only find a correlation between $\alpha_{OX}$
and $\dot{\mathcal{M}}$ for sources with $\dot{\mathcal{M}} >
\dot{\mathcal{M}}_{c}$. In such cases, the faster accreting sources appear to
have systematically larger $\alpha_{OX}$ values. iii) We also find that the
torus in the faster accreting systems seems to be less efficient in
reprocessing the primary AGN radiation having lower IR-to-optical spectral
slopes.
  These findings, failing to recover the predicted differences between the SEDs
of slim and thin ADs within the observed spectral window, suggest that
additional physical processes or very special geometry act to reduce the
extreme UV radiation in fast accreting AGN. This may be related to photon
trapping, strong winds, and perhaps other yet unknown physical processes.
