In the path towards a muon collider with center of mass energy of 10 TeV ormore, a stage at 3 TeV emerges as an appealing option. Reviewing the physicspotential of such muon collider is the main purpose of this document. In orderto outline the progression of the physics performances across the stages, a fewsensitivity projections for higher energy are also presented. There are manyopportunities for probing new physics at a 3 TeV muon collider. Some of themare in common with the extensively documented physics case of the CLIC 3 TeVenergy stage, and include measuring the Higgs trilinear coupling and testingthe possible composite nature of the Higgs boson and of the top quark at the 20TeV scale. Other opportunities are unique of a 3 TeV muon collider, and stemfrom the fact that muons are collided rather than electrons. This isexemplified by studying the potential to explore the microscopic origin of thecurrent g-2 and B-physics anomalies, which are both related with muons.<br
