We theoretically investigate integrated photonic resonators formed by two mutually coupled Sagnac loop reflectors (MC-SLRs). Mode interference in the MC-SLR resonators is tailored to achieve versatile filter shapes with high performance, which enable flexible spectral engineering for diverse applications. By adjusting the reflectivity of the Sagnac loop reflectors (SLRs) as well as the coupling strength between different SLRs, we achieve optical analogues of Fano resonance with ultrahigh spectral slope rates, wavelength interleaving / non-blocking switching functions with significantly enhanced filtering flatness, and compact bandpass filters with improved roll-off. In our designs the requirements for practical applications are considered, together with detailed analyses of the impact of structural parameters and fabrication tolerances. These results highlight the strong potential of MC-SLR resonators as advanced multi-functional integrated photonic filters for flexible spectral engineering in optical communications systems.