Extreme mass-ratio inspirals (EMRIs) are binary systems where a compact object slowly inspirals into its much larger compact partner (i.e., a galactic center supermassive black hole [SMBH]). Since we anticipate such systems to exist within and be dynamically influenced by the galactic center environment, we expect them to be instrumental in studying these environments and testing our theories of gravity in the strong field regime. The gravitational waves associated with the EMRI motion fall within the mHz regime, making them target sources for future space-based detectors. However, because of the crowded nature of these galactic centers, these EMRIs could be perturbed by other nearby orbiting bodies. This paper focuses on cataloging potential perturbations in EMRIs due to a third-body perturber near resonance. We use the formalism and code tools developed in the previous paper in this series [Silva and Hirata, Phys. Rev. D 106, 084508 (2022)] and expand them to account for a general outer body orbit, allowing for multiple resonant interactions within an orbit and across a variety of SMBH spins. We find that, after investigating nearly 142,000 resonant interactions across a restricted set of 180 different simulated orbit systems, none cause changes to the EMRI dynamics beyond a perturbative correction ($\lesssim 1\%$ to the action variables), but could lead to potentially large changes in the phase of the waveform of order 0.1 radian. Detectable phase changes in the waveform induced by third-body perturbers could therefore be a common occurrence and will require careful consideration for developing accurate EMRI waveform models. This analysis suggests that our formalism and pipeline are robust enough to handle a wide variety of resonances from various perturbing orbit configurations around the EMRI, which will aid in developing more accurate waveform models to better probe galactic center environments and test theories of gravity using gravitational wave observations of EMRIs.

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• Experimental studies of gravity
• General relativity
• Gravitational waves