The Cantor alloy CrFeCoMnNi is generally fcc structured, but moderate changes in the composition can have a large influence on the phase formation. The aim of this study was to understand the changes brought on in low-nitrogen-containing (CrFeCo)1-yNy thin films with y = 0.19 on the addition of copper, an interesting metal in terms of atomic size and nitride formation enthalpy. (CrFeCoCux)1-yNy films were grown by reactive magnetron sputtering. The amount of copper in the films was increased from x = 0 to x = 0.15 to study competitive phase formation. Without Cu, two-phase fcc + bcc films were obtained. The addition of Cu was found to stabilize the bcc structure despite the fact that Cu as a pure metal is fcc. Nanoindentation tests showed slight increase in hardness with initial Cu addition from 11 GPa to 13.7 ± 0.2 GPa. The occurrence of pile up as opposed to cracking is an indication of the film’s ductility.