Muon colliders have the unique potential to reach the highest collision energies at a lepton machine, allowing unprecedented physics exploration in direct searches of new heavy states and high-precision tests of standard phenomena. The International Muon Collider Collaboration IMCC, hosted at CERN, is gathering the community to prepare the baseline design study of a multi-TeV muon collider reaching the center of mass energy of 10 TeV or more. This facility can improve significantly on other energy-frontier colliders, in terms of footprint, cost, power consumption and time scale. The physics reach strongly relies on the mitigation of the background induced by muon beam decays, demanding for optimization of the machine interaction region and the detector design. The status of the project, future plans and synergies will be discussed.