Calcium carbonate is a relevant constituent of the Earth's crust that is transferred into the deep Earth through the subduction process. Its chemical interaction with calcium-rich silicates at high temperatures give rise to the formation of mixed silicate-carbonate minerals, but the structural behavior of these phases under compression is not known. Here we report the existence of a dense polymorph of Ca5(Si2O7)(CO3)2 tilleyite above 8 GPa. We have structurally characterized the two phases at high pressures and temperatures, determined their equations of state and analyzed the evolution of the polyhedral units under compression. This has been possible thanks to the agreement between our powder and single-crystal XRD experiments, Raman spectroscopy measurements and ab-initio simulations. The presence of multiple cation sites, with variable volume and coordination number (6-9) and different polyhedral compressibilities, together with the observation of significant amounts of alumina in compositions of some natural tilleyite assemblages, suggests that post-tilleyite structure has the potential to accommodate cations with different sizes and valencies.