Multilevel converters have enabled various applications that are not possible with conventional two-level converters. Many of these applications, however, need a high output bandwidth, often approaching the switching rate limit of the transistors, with high quality, e.g., to actively stabilize and dampen a DC grid or specifically excite certain molecules or neural circuits in medical applications. A high bandwidth approaching the switching rate challenges existing modulation methods: carrier-based switching modulation is fine at low frequencies but experiences interaction between the carrier and the signal at the upper end of the spectrum; fundamental-frequency switching, such as nearest-level modulation (NLM), perform well at high frequencies but cause intolerable distortion for low frequency contents. We propose a hybrid modulation concept that can combine any methods from these two classes. It passes the error of a fundamental frequency method through a filtered switching modulator to combine the high output quality of the latter with the high bandwidth of the former. We optimize the filter to avoid under-modulation of the signal with the carrier of the modulator and to achieve the minimum overall distortion throughout a wide output bandwidth. We demonstrate the performance experimentally with a cascaded-bridge converter and compare it with the best prior arts. This technique ensures a usable output bandwidth up to 100% of the switching rate and maintains a total distortion level below 3%.