Composite operators in $\mathcal{N}=4$ Super Yang-Mills

We consider four-point functions of protected, double- and single-trace operators in the large central charge limit. We use superconformal symmetry to disentangle the contribution of protected operators in the partial wave decomposition. With this information, we fix the non protected part of such correlators up to subleading order in the large central charge expansion. We particularly focus on the triple-trace sector of the correlator and comment on the connection to the holographic description of these correlators.