Integrated nested microring resonators (NMRRs) with multiple split resonances are theoretically investigated for advanced spectral engineering. First, the spectral response of NMRRs of different orders is systematically analyzed, revealing the evolution of extinction ratio (ER), quality (Q) factor, and mode-splitting degree with device structural parameters. Next, the split resonances of NMRRs are engineered to realize different filter functions with outstanding performance, including dense wavelength division multiplexing (DWDM) and Fano filtering. The former enables reduced channel spacing by a factor of ~18 without increasing the device footprint, whereas the latter achieves high slope rates (SRs) of up to ~1337 and ~1616 dB/nm while maintaining low insertion losses (ILs) of 3 and 5 dB, respectively. Finally, fabrication tolerances and practical limitations are analyzed to guide the design and optimization of NMRRs, together with discussion on their potential for other applications. These results highlight the strong potential of NMRRs as highly versatile integrated photonic filters with flexible spectral engineering capabilities.