The feasibility of 3-bits per cell storage in self-referenced thermally assisted magnetic random access memories is demonstrated both by macrospin simulations and experiments. The memory dot consists of a storage layer where CoFe/CoFeB magnetization direction is pinned by an IrMn layer using the ferromagnet/antiferromagnet interfacial exchange coupling, separated by an MgO tunnel barrier from a CoFeB sense layer whose magnetization direction is free to rotate. Writing is performed by heating the antiferromagnet above its blocking temperature by sending a current pulse through the magnetic tunnel junction, with the application of an in-plane field during the subsequent cooling phase, thus setting the new storage layer pinning direction. This pinning direction actually carries the information stored in the storage layer. Reading is performed by applying a rotating field, inducing a coherent rotation of the sense layer, and subsequently locating the field angle associated with the minimum measured resistance. This angle corresponds to the parallel magnetic configuration of the magnetic tunnel junction and therefore allows determining the pinning direction established during the write operation. The number of distinguishable pinning angles defines the total number of bits that can be stored in a single dot.