Sagnac interferometers have important applications in the field of optical filtering. Based on the 3D silicon nitride waveguide platform, we obtained a new Sagnac-like resonance filter system by using a two-layer multi-microring system. In the new system, the bottom main microring cavity was coupled via feedback with the top input/output waveguide and the single/double sub-microrings, respectively. Furthermore, two light waves transmitting in the opposite direction were generated in the coupling area and interfered with each other, thereby a filter structure with adjustable filtering waveforms and resonance peak positions is realized. In this paper, a transmission matrix and an iteration method were used to analyze the output spectra, and the output waveform was designed by changing the coupling coefficient between the waveguide and the microcavity. Besides, the phase of the main microcavity was modulated by the metal heating electrode to regulate the resonance peak position. The theoretical analysis and experimental characterization results show that the dense filtering effect of the device can be effectively improved by adding top sub-microrings and thus the 3D integrated structure can provide greater design freedom. The related multi-microring resonance filter system can be widely used in optical communication, optical sensing, and other fields.