This article considers the problem of intercellular interference cancellation for downlink MC-CDMA systems. Throughout this work, we mainly focus on parallel interference cancellation (PIC) techniques due to the low latency they present. After deriving a version of a classical PIC receiver, suitably tuned to take into account the intercellular interference, we propose another two different approaches in order to mitigate its effects. Finally, with several simulation results we demonstrate the significant performance improvements of the proposed schemes over a wide signal to interference ratio (SIR) area.