High pressure X-ray diffraction, Raman scattering, and electrical measurements, together with theoretical calculations, which include the analysis of the topological electron density and electronic localization function, evidence the presence of an isostructural phase transition around 2 GPa, a Fermi resonance around 3.5 GPa, and a pressure-induced decomposition of SnSb2Te4 into the high-pressure phases of its parent binary compounds (alpha-Sb2Te3 and SnTe) above 7 GPa. The internal polyhedral compressibility, the behavior of the Raman-active modes, the electrical behavior, and the nature of its different bonds under compression have been discussed and compared with their parent binary compounds and with related ternary materials. In this context, the Raman spectrum of SnSb2Te4 exhibits vibrational modes that are associated but forbidden in rocksalt-type SnTe; thus showing a novel way to experimentally observe the forbidden vibrational modes of some compounds. Here, some of the bonds are identified with metavalent bonding, which were already observed in their parent binary compounds. The behavior of SnSb2Te4 is framed within the extended orbital radii map of BA(2)Te(4) compounds, so our results pave the way to understand the pressure behavior and stability ranges of other "natural van der Waals" compounds with similar stoichiometry.