We analyse the CFT-data of planar 4D \(\mathcal{N}\) = 4 Super-Yang-Mills theory at strong coupling. By combining spectral data extracted from integrability, with recent advances in computing the AdS Virasoro-Shapiro amplitude, we extract predictions for leading order OPE coefficients on entire Kaluza-Klein (KK-)towers of states. We observe that the appropriately normalised leading order OPE coefficients for all states in a given KK-tower are the same. Furthermore, we also notice that, in many cases, the leading order OPE coefficients of all states in the KK-tower vanish, suggesting a simplification of the physics in this limit.
