We report the discovery of two warm exoplanets orbiting the cool binary system TOI-2267, composed of the M5 (TOI-2267A) and M6 (TOI-2267B) stars, whose angular separation is 0.384 arcsec, corresponding to a projected distance of only about 8 au at 22 pc from the Solar System. To confirm the planetary nature of these objects, we combined photometry from the Transiting Exoplanet Survey Satellite (TESS) and ground-based facilities together with high-resolution images, archival data, and statistical validation in our analyses. From the current data set, we cannot unambiguously determine which star of the binary the planets orbit. These planets are Earth-sized with radii of 1.00±0.11 and 1.14±0.13 R⊕ for TOI-2267 b (P = 2.28 d) and TOI-2267 c (P = 3.49 d), respectively, when orbiting TOI-2267A, whereas the radii are of 1.22±0.29 and 1.36±0.33 R⊕ when orbiting TOI-2267B. In addition to the signals attributed to TOI-2267 b and c, the TESS data reveal a third strong signal with a periodicity of 2.03 d (TOI-2267.02). Although statistical analyses support its planetary nature, ground-based follow-up observations did not detect this signal. Its status therefore remains that of a planetary candidate, with an Earth-size of 0.95±0.12 R⊕ or 1.13±0.30 R⊕ when orbiting TOI-2267A or B, respectively. If this candidate is confirmed, dynamical analyses indicate that all three planets cannot orbit the same star. The most plausible configurations are b–c or .02–c orbiting the same star, while the .02–b case is unlikely due to strong instabilities. The proximity of b and c to a first-order 3:2 mean motion resonance suggests they likely orbit the same star, with .02 orbiting the other component. This scenario would make TOI-2267 the most compact binary system known to host planets, with both components harbouring transiting worlds, and offer a unique benchmark for studying planet formation and evolution in compact binary environments.