Stellar multiplicity is a common consequence of the stellar formation process. Low-mass stars are the prime constituent of the nearby stellar population, with late-type accounting for the majority of the hydrogen-fusing objects in the Solar neighborhood. The CARMENES input catalogue of M dwarfs (Carmencita) is a comprehensive and homogeneous sample of M dwarfs, with more than 2200 well-characterised main sequence stars, and therefore constitutes a solid basis for the investigation of the multiplicity of these stars. We search for physical companions at all physical separations, from close-orbiting spectroscopic binaries to very wide common proper motion pairs, up to 200 000 au apart from each other. For this, we make extensive use of the latest data from Gaia DR3 together with published measurements from the literature. We find that the multiplicity rate in these stars can be as high as 40%, given that candidate systems hinted by Gaia are eventually resolved.