A diversity scheme with Fractional Sampling (FS) in OFDM receivers has been investigated recently. FS path diversity makes use of the imaging components of the desired signal transmitted on the adjacent channel. To increase the diversity gain with FS the bandwidth of the transmit signal has to be enlarged. This leads to the reduction of spectrum efficiency. In this paper non-orthogonal access over multiple channels in the frequency domain with iterative interference cancellation (IIC) and FS is proposed. The proposed scheme transmits the imaging component non-orthogonally on the adjacent channel. In order to accommodate the imaging component, it is underlaid on the other desired signal. Through diversity with FS and IIC, non-orthogonal access on multiple channels is realized. Our proposed scheme can obtain diversity gains for non-orthogonal signals modulated with QPSK.