A solution to the MiniBooNE excess invoking rare three-body decays of the charged pions and kaons to new states in the MeV mass scale was recently proposed as a dark-sector explanation. This class of solution illuminates the fact that, while the charged pions were focused in the target-mode run, their decay products were isotropically suppressed in the beam-dump-mode run in which no excess was observed. This suggests a new physics solution correlated to the mesonic sector. We investigate an extended set of phenomenological models that can explain the MiniBooNE excess as a dark sector solution, utilizing long-lived particles that might be produced in the three-body decays of the charged mesons and the two-body anomalous decays of the neutral mesons. Over a broad set of interactions with the long-lived particles, we show that these scenarios can be compatible with constraints from LSND, KARMEN, and MicroBooNE, and evaluate the sensitivity of the ongoing and future data taken by the Coherent CAPTAIN Mills experiment to a potential discovery in this parameter space. Published by the American Physical Society 2024