Exploration of potential planetary perturbers responsible for the observed TTV signal in the HD 332231 system. Upper panels: map of simulated configurations in the parameter space of perturber’s orbital period and eccentricity. Red pixels denote solutions that reproduce both the observed TTV period and amplitude while remaining below the RV detection threshold. Violet pixels indicate configurations that match the TTV signal and may be confirmed with the current RV data. Yellow regions correspond to dynamically unstable (orbit-crossing) configurations. Middle panels: Negative log-likelihood metric, −ln ℒ, as a function of the perturber’s orbital period for various resonance zones. The horizontal dashed line indicates the −ln ℒ value for a single-planet model. Bottom panels: perturber mass required to reproduce the observed A_TTV across the tested orbital periods. Orange points and dotted vertical lines indicate the three illustrative solutions presented in Fig. 4.