A clutch mechanism that is configured to be driven in rotation about an axis and includes two assemblies, each assembly including at least an outer disc carrier externally delimiting a cavity, a clutch comprising a stack of coupling discs, and friction discs, the stack being housed in the cavity and configured to be driven in rotation about the axis, a reaction member configured to allow compression of the coupling discs against the friction discs in an engaged position of the clutch, the clutch mechanism comprising at least one device for assembling the two assemblies, the clutch mechanism including at least one device for adjusting an axial distance between the two clutches.