Converting energy efficiently from renewable sources is crucial; however, the large-scale implementation of technologies such as e-mobility and wind turbine but also magnetic refrigeration will increase drastically the material intensity of strategic metals like rare-earths (RE) and cobalt. Magnets are key enablers of a net-zero emission scenario. As conversion technologies become more advanced, the required attributes of the magnets are now much more demanding and multifunctional, additionally required mechanical, thermal, mechanical stabilities will increase efficiency and lifetime of the devices. We live now in a cryogenic age and gas-compression cooling has not been changed for a century, with only incremental efficiency improvements over time. Magnetic refrigeration uses not only Nd-based permanent magnets, the same as used for the e-motor, to drive the magnetic heat pump but also heavy REs such as Gd for the magnetocaloric heat exchanger. In the CoCoMag proposal, we are targeting these two main applications, e-mobility and magnetic refrigeration, by implementing a disruptive approach for magnet design. Our idea is the use of compositionally complex alloys (CCA) based on hexagonal Fe2P- and MM´X-type compounds, derived from high entropy alloys, for the development of both permanent magnet and magnetocaloric materials without critical elements. With CCA, we can fully utilize the large degrees of freedom in the compositional space in a multi-element approach, leaving behind traditional metal alloying practised since Bronze Age. Using CCA, we address the primary magnetic properties AND the above equally important secondary engineering properties. We will use the theoretical predictions, experimental validation and machine learning cycle to reach our goals fast. Being successful with CoCoMag, we will be give answers to challenges on the path to the decarbonization and electrification of mobility and energy sectors using new magnets free of critical elements.