Two classes of RF/microwave planar quad-band bandpass filters (BPFs) that simultaneously exploit transversal signal-interference and multi-passband-splitting mechanisms are reported. The first approach makes use of a triple-band bandpass transversal filtering section (TFS) composed of two in-parallel stepped-impedance coupled-line signalpropagation paths.By inserting an open-ended stub at the input and output terminals of this TFS, its middle passband is divided into two sub-bands to attain an overall quadpassband filtering response. The second configuration employs a dual-passband TFS based on a coupled-line directional coupler with open-ended stubs at its direct and coupled ports. By loading such TFS with a replica of it at the direct and coupled ports of its coupler, the two passbands are split into four sub-bands to obtain the quad-band functionality. The RF operational foundations of these quad-band BPFs, along with single-and multi-stage design examples featuring sharp-rejection four-passband filtering responses with transmission zeros (TZs), are detailed. Moreover, for experimentaldemonstration purposes, two microstrip prototypes are developed and tested. Besides, as a further application, a two-layer balanced-circuit version with ultra-broad commonmode (CM) suppression of the constituent triple-passband TFS of the first prototype is built and measured.