Schematics of the effect of apsidal precession and external modulations on O–C diagrams. The upper panels show the case of a Keplerian EMRI orbit (left) and of a General Relativistic one including apsidal precession (right). The lower two panels are associated with the two modulating scenarios we considered in our work: disc precession (left) and a hierarchical triple model in which an outer SMBH forms a tight SMBH binary with the inner EMRI system (right), see text for details.