The MultiLevel Physical Optics (MLPO) algorithm is extended for fast and accurate analysis of multi-reflector antennas. To that end, a near-field version of the MLPO algorithm for field propagation between reflectors is proposed and combined with the earlier developed generalized far-field MLPO. The computational complexity of the near-field MLPO is comparable to that of its far-field counterpart. The performance of the proposed method is studied on the example of RATAN-600 radio telescope antenna.