  Electron-doped Eu(Fe$_{0.93}$Rh$_{0.07}$)$_2$As$_2$ has been systematically
studied by high pressure investigations of the magnetic and electrical
transport properties, in order to unravel the complex interplay of
superconductivity and magnetism. The compound reveals an exceedingly broad
re-entrant transition to the superconducting state between $T_{\rm{c,on}} =
19.8$ K and $T_{\rm{c,0}} = 5.2$ K due to a canted A-type antiferromagnetic
ordering of the Eu$^{2+}$ moments at $T_{\rm{N}} = 16.6$ K and a re-entrant
spin glass transition at $T_{\rm{SG}} = 14.1$ K. At ambient pressure evidences
for the coexistence of superconductivity and ferromagnetism could be observed,
as well as a magnetic-field-induced enhancement of the zero-resistance
temperature $T_{\rm{c,0}}$ up to $7.2$ K with small magnetic fields applied
parallel to the \textit{ab}-plane of the crystal. We attribute the
field-induced-enhancement of superconductivity to the suppression of the
ferromagnetic component of the Eu$^{2+}$ moments along the \textit{c}-axis,
which leads to a reduction of the orbital pair breaking effect. Application of
hydrostatic pressure suppresses the superconducting state around $14$ kbar
along with a linear temperature dependence of the resistivity, implying that a
non-Fermi liquid region is located at the boundary of the superconducting
phase. At intermediate pressure, an additional feature in the resistivity
curves is identified, which can be suppressed by external magnetic fields and
competes with the superconducting phase. We suggest that the effect of negative
pressure by the chemical Rh substitution in
Eu(Fe$_{0.93}$Rh$_{0.07}$)$_2$As$_2$ is partially reversed, leading to a
re-activation of the spin density wave.
