Ni-Mn-Ga is interesting as a prototype of a magnetic shape-memory alloy showing large magnetic-field-induced strains. We present here results for the magnetic ordering of Mn-rich Ni-Mn-Ga alloys based on both experiments and theory. Experimental trends for the composition dependence of the magnetization are measured by a vibrating sample magnetometer in magnetic fields of up to several tesla and at low temperatures. The saturation magnetization has a maximum near the stoichiometric composition and it decreases with increasing Mn content. This unexpected behavior is interpreted via first-principles calculations within the density-functional theory. We show that extra Mn atoms are antiferromagnetically aligned to the other moments, which explains the dependence of the magnetization on composition. In addition, the effect of Mn doping on the stabilization of the structural phases and on the magnetic anisotropy energy is demonstrated.