Commercial magnetic memories rely on the bistability of ordered spins in ferromagnetic materials. Recently, experimental bistable memories have been realized using fully compensated antiferromagnetic metals. Here we demonstrate a multiple-stable memory device in epitaxial MnTe, an antiferromagnetic counterpart of common II-VI semiconductors. Favourable micromagnetic characteristics of MnTe allow us to demonstrate a smoothly varying zero-field antiferromagnetic anisotropic magnetoresistance (AMR) with a harmonic angular dependence on the writing magnetic field angle, analogous to ferromagnets. The continuously varying AMR provides means for the electrical read-out of multiple-stable antiferromagnetic memory states, which we set by heat-assisted magneto-recording and by changing the writing field direction. The multiple stability in our memory is ascribed to different distributions of domains with the Néel vector aligned along one of the three magnetic easy axes. The robustness against strong magnetic field perturbations combined with the multiple stability of the magnetic memory states are unique properties of antiferromagnets.