We combined synchrotron-based infrared absorbance and Raman scattering spectroscopies with diamond anvil cell techniques and a symmetry analysis to explore the properties of multiferroic (NH4)2FeCl5·H2O under extreme pressure-temperature conditions. Compression-induced splitting of the Fe-Cl stretching, Cl-Fe-Cl and Cl-Fe-O bending, and NH4+ librational modes defines two structural phase transitions, and a group-subgroup analysis reveals space group sequences that vary depending upon proximity to the unexpectedly wide order-disorder transition. We bring these findings together with prior high-field work to develop the pressure-temperature-magnetic field phase diagram uncovering competing polar, chiral, and magnetic phases in this system.