In multiuser access visible light communication (VLC) systems, many multiplex techniques can be utilized to fully exploit the limited bandwidth. In frequency-division multiplexing systems, one possible solution is to dynamically allocate limited bandwidth resources for users to support multiple-service access. To enable high-speed transmissions, the super-Nyquist multiband concept has been proposed in recent years. Specifically, the center frequency spacing is narrowed, and the subcarriers are nonorthogonally overlapped to enable more services and users in multiband systems. Studies have shown that this strategy can support higher spectral efficiency (SE) while simultaneously, introducing intersymbol interference (ISI) and intercarrier interference (ICI). Therefore, a well-designed ICI mitigation scheme is required. In multiband carrierless amplitude phase (m-CAP) modulation systems, it is technically challenging to achieve the SE beyond one baud/s/Hz under the pre-forward error correction (pre-FEC) threshold without increasing the modulation order. Inspired by the distinctive pulse shaping filter (PSF) structure in a non-orthogonal m-CAP scheme, we propose the iterative decision feedback kurtosis minimum (DFKM) scheme and achieve the super-Nyquist SE of approximately 1.06 baud/s/Hz. In contrast to existing ICI mitigation schemes, the theoretical framework reveals that symbol-level crosstalk filters are indispensable to reap the benefit of super-Nyquist transmission, not limited to VLC.