  Relative cross sections for $m$-fold photoionization ($m=1,\ldots,5$) of
Fe$^{3+}$ by single photon absorption were measured employing the photon-ion
merged-beams setup PIPE at the PETRA III synchrotron light source operated at
DESY in Hamburg, Germany. The photon energies used spanned the range of
$680-950\,\mathrm{eV}$, covering both the photoexcitation resonances from the
$2p$ and $2s$ shells as well as the direct ionization from both shells.
Multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations were performed to
simulate the total photoexcitation spectra. Good agreement was found with the
experimental results. These computations helped to assign several strong
resonance features to specific transitions. We also carried out Hartree-Fock
calculations with relativistic extensions taking into account both
photoexcitation and photoionization. Furthermore, we performed extensive MCDHF
calculations of the Auger cascades that result when an electron is removed from
the $2p$ and $2s$ shells of Fe$^{3+}$. Our theoretically predicted charge-state
fractions are in good agreement with the experimental results, representing a
substantial improvement over previous theoretical calculations. The main reason
for the disagreement with the previous calculations is their lack of inclusion
of slow Auger decays of several configurations that can only proceed when
accompanied by de-excitation of two electrons. In such cases, this additional
shake-down transition of a (sub-)valence electron is required to gain the
necessary energy for the release of the Auger electron.
