The　protection　against　seismic　hazards　for　rigid　block-like　structures,　commonly　modeled　as　rigid　blocks,　is　often　achieved　by　coupling　such　structures　with　external　protection　devices.　The　most　commonly　used　protection　devices　include　dynamic　mass　absorbers,　oscillating　masses,　base　isolation　systems,　and　hysteretic　mass　damper　inerters.　Additionally,　several　papers　have　studied　the　dynamic　and　seismic　response　of　rigid　blocks　connected　in　series,　with　most　of　them　focusing　on　the　stacked　rigid　block　system,　where　the　blocks　are　placed　one　on　top　of　the　other.　This　paper　investigates　the　seismic　behavior　of　a　system　consisting　of　two　rigid　blocks　connected　in　series　through　a　linear　visco-elastic　Maxwell　device.　The　aim　is　to　understand　the　possibility　of　improving　the　seismic　response　of　a　rocking　structure　(modeled　by　one　of　the　two　rigid　blocks)　by　connecting　it　with　a　rocking　protection　device　(modeled　by　the　additional　rigid　block).　Each　rigid　block　can　exhibit　three　different　types　of　motion:　full　contact,　rocking　motion　around　the　left　base　vertex,　and　rocking　motion　around　the　right　base　vertex.　Consequently,　during　the　motion　of　the　coupled　system,　nine　different　combinations　can　occur,　each　of　which　is　described　through　a　specific　set　of　equations　of　motion.　A　parametric　analysis　is　performed　with　the　aim　of　investigating　how　the　characteristics　of　the　additional　rigid　block　and　connection　device　affect　the　seismic　behavior　of　the　main　rigid　block　(the　one　modeling　the　rocking　structure).　The　assessment　is　carried　out　through　a　comparison　between　the　displacements　of　the　coupled　system　and　those　of　the　stand-alone　blocks.　The　results,　organized　in　gain　maps,　show　that　there　are　several　combinations　of　the　characteristics　of　the　additional　rigid　block　and　connection　device　that　lead　to　an　improvement　in　the　seismic　behavior　of　the　main　rigid　block.