Since the seminal paper by Arikan, polar codes have been generalized in a wide range of directions. However, construction of polar codes for magnetic recording channels remains an open problem. In this work, we consider the use of multilevel code (MLC) design with a multistage decoding (MSD) algorithm where independent polar codes of different rates are interleaved at the encoder. Since the MLC-MSD scheme allows the decoder to assume that the equivalent sub-channels for each codeword are memoryless, encoding/decoding methods designed for polar codes for binary memoryless channels can be used. We show that only a small number of interleaves are needed for rates close to the SIR. We then construct high-rate polar codes and demonstrate the performance of these codes in the MLC-MSD scheme.