Orthogonal frequency-division multiplexing (OFDM) systems over rapidly time varying channels may suffer from significant inter-carrier interference (ICI), which destroys the orthogonality between subcarriers and degrades the detection performance. Without sufficient ICI suppression, OFDM systems usually experience an error floor. According to the approximate matched filter bound (AMFB), the error floor in a coded OFDM system is not irreducible. In this work, we introduce novel multiple feedback matched filter (MBMF)-based ICI cancellation receivers. Based on the output of a novel MBMF scheme, the approach employs a multiple ICI cancellation strategy with or without signal-to-interference-plus-noise-ratio (SINR) ordering. The developed schemes can significantly improve the performance and remove the error floor with a negligible complexity increase. Given the multiple cancellation approach, we compare the SINR performance of the MBMF outputs with that employing single feedback and show that the SINR performance with multiple cancellation candidates is improved over that with a single one at practical SNR values. Additionally, for time-varying channels, we exploit partial fast Fourier transform (PFFT) by splitting one OFDM symbol into multiple segments; the channel state is separately estimated by least-squares (LS) methods without inserting more pilots. Simulation results demonstrate the superiority of the proposed methods over serial and block equalizers and the robustness to the Doppler effects compared to conventional single-segment method.