In this work, we demonstrate, through first-principles calculations, the existence of a new family of copper-based MXenes. These add up new structures to the previously reported universe and span the interest of such 2D materials for applications in heterogeneous catalysis, ion-based batteries, sensors, biomedical applications, and so on. First, we propose the MXene-like structures: Cu2N, Cu2C, and Cu2O. Phonon spectra calculations confirmed their dynamical stability by showing just positive frequencies all through the 2D Brillouin zone. The new MXenes family displays metallic characteristics, mainly induced by the Cu-3d orbitals. Bader charge analysis and charge density differences depict bonds with ionic character in which Cu is positively charged, and the non-metal atom gets an anionic character. Also, we investigate the functionalization of the proposed structures with Cl, F, O, and OH groups. Results show that the H3 site is the most favorable for functionalization. In all cases, the non-magnetic nature and metallic properties of the pristine MXenes remain. Our results lay the foundations for the experimental realization of a new MXenes family.