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.
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