Quaternary kesterite-type (KS) compounds have attracted worldwide attention from the scientific community as promising materials for solar cells. On the route to optimizing their performance, the effect of stress and strain constitutes a critical factor when it comes to thin film applications. Following a recent theoretical study, we report here joint experimental and computational high-pressure investigations on the KS Ag2ZnSnS4 and wurtz–kesterite (WZ–KS)-type Ag2CdSnS4 compounds. Our results reveal that both materials undergo successive transformations, first into a GeSb-type and then toward a CrN-type modification at ambient temperature. Our theoretical calculations predict a metallic character for all Ag2ZnSnS4 and Ag2CdSnS4 high-pressure phases. In addition, structural disorder is observed in KS Ag2ZnSnS4 upon moderate compression, prior to its KS → GeSb-type transition. Decompression leads to the recovery of a disordered zinc blende-type structure in the latter, whereas Ag2CdSnS4 retains the disordered GeSb-type modification. The similarities and deviations from the archetypical KS Cu2ZnSnS4 are discussed.