Random quenched dilution of the triangular-lattice antiferromagnetic Ising model locally relieves frustration, leading to ordering phenomena. We have studied this system, under such dilution of one sublattice, using hard-spin mean-field theory. After a threshold dilution, two sublattices develop nonzero magnetizations of equal magnitude and opposite signs, as all three sublattices exhibit. spin-glass order. In this phase, multiple sets of ordered solutions occur. A phase diagram is obtained in dilution fraction and temperature.