We study the problem of unsourced random access (URA) over Rayleigh block-fading channels with a receiver equipped with multiple antennas. We employ multiple stages of orthogonal pilots, each of which is randomly picked from a codebook. In the proposed scheme, each user encodes its message using a polar code and appends it to the selected pilot sequences to construct its transmitted signal. Accordingly, the received signal consists of superposition of the users’ signals each composed of multiple orthogonal pilot parts and a polar coded part. We use an iterative approach for decoding the transmitted messages along with a suitable successive interference cancellation scheme. Performance of the proposed scheme is illustrated via extensive set of simulation results which show that it significantly outperforms the existing approaches for URA over multiple-input multiple-output fading channels.