Sara Gliorio, Matteo Della Rocca, Susanna Barsanti, Leonardo Gualtieri, Andrea Maselli, Thomas P. Sotiriou

We investigate the dynamics of asymmetric binaries in extensions of General Relativity featuring a massless scalar field non-minimally coupled to gravity, focusing on the interplay between eccentricity and inclination in fully generic bound orbits. Building on an effective field theory framework tailored to extreme- and intermediate-mass-ratio inspirals, we compute scalar-field perturbations using a new arbitrary-precision C++ code capable of evolving perturbations along generic Kerr geodesics, STORM. We investigate the complete set of scalar fluxes at infinity and through the horizon across the relevant parameter space and analyze their harmonic structure as a function of orbital geometry and black-hole spin. Our results advance ongoing efforts to construct accurate waveform models for asymmetric binaries beyond GR and lay the groundwork for precision tests of fundamental physics with next-generation gravitational-wave detectors.