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In the main ring (MR) of the Japan Proton Accelerator Research Complex (J-PARC), an upgrade project of the Trim-S system is in progress to further mitigate beam loss. The correction strategy targets major resonances affecting both on- and off-momentum particles on the third-order resonances 3vx = 64 and vx + 2vy = 64. Previous investigations using 8 sets of Trim-S units did not identify new resonance sources for off-momentum particles, as 8 sets do not provide sufficient degrees of freedom to simultaneously correct resonances for both momentum components. With 4 additional Trim-S sets now newly prepared, experiments with a total of 12 sets are feasible for the next steps. For a preliminary evaluation of the 12-set configuration, quantifying the strength of the target third-order resonances for off-momentum particles is essential. In this paper, we report the evaluation method and results of the third-order resonance strength analysis for off-momentum particles in the J-PARC MR.
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