The IceCube-Gen2 Neutrino Observatory is proposed to extend the all-flavour energy range of IceCube beyond PeV energies. It will comprise two key components: I) An enlarged 8$\,$km$^3$ in-ice optical Cherenkov array to measure the continuation of the IceCube astrophysical neutrino flux and improve IceCube's point source sensitivity above $\sim\,$100$\,$TeV; and II) A very large in-ice radio array with a surface area of about 500$\,$km$^2$. Radio waves propagate through ice with a kilometer-long attenuation length, hence a sparse radio array allows us to instrument a huge volume of ice to achieve a sufficient sensitivity to detect neutrinos with energies above tens of PeV.

The different signal topologies for neutrino-induced events measured by the optical and in-ice radio detector - the radio detector is mostly sensitive to the cascades produced in the neutrino interaction, while the optical detector can detect long-ranging muon and tau leptons with high accuracy - yield highly complementary information. When detected in coincidence, these signals will allow us to reconstruct the neutrino energy and arrival direction with high fidelity. Furthermore, if events are detected in coincidence with a sufficient rate, they resemble the unique opportunity to study systematic uncertainties and to cross-calibrate both detector components.

We present the expected rate of coincidence events for 10 years of operation. Furthermore, we analyzed possible detector optimizations to increase the coincidence rate.