Context. Multiplicity studies greatly benefit from focusing on M dwarfs because they are often paired in a variety of configurations with both stellar and substellar objects, including exoplanets. Aims. We aim to address the observed multiplicity of M dwarfs by conducting a systematic analysis using the latest available astropho-tometric data. Methods. For every star in a sample of 2214 M dwarfs from the CARMENES catalogue, we investigated the existence of resolved and unresolved physical companions in the literature and in all-sky surveys, especially in Gaia DR3 data products. We covered a very wide range of separations, from known spectroscopic binaries in tight arrangements (~0.01 au) to remarkably separated ultra-wide pairs (~105 au). Results. We identified 835 M dwarfs in 720 multiple systems, predominantly binaries. Thus, we propose 327 new binary candidates based on Gaia data. If these candidates are finally confirmed, we expect the multiplicity fraction of M dwarfs to be 40.3‑2.0+2.1%. When only considering the systems already identified, the multiplicity fraction is reduced to 27.8‑1.8+1.9%. This result is in line with most of the values published in the literature. We also identified M-dwarf multiple systems with FGK, white dwarf, ultra-cool dwarf, and exoplanet companions, as well as those in young stellar kinematic groups. We studied their physical separations, orbital periods, binding energies, and mass ratios. Conclusions. We argue that based on reliable astrometric data and spectroscopic investigations from the literature (even when considering detection biases), the multiplicity fraction of M dwarfs could still be significantly underestimated. This calls for further high-resolution follow-up studies to validate these findings.