Fano resonances in plasmonic nanostructures are important for plasmon line shaping. Compared to a single Fano resonance, multiple Fano resonances can modify plasmon lines at several spectral positions simultaneously, but they often suffer from weak modulation depths. In this paper, plasmonic heptamer clusters comprising split nanorings are designed to form multiple Fano resonances. Three prominent Fano resonances are observed in the spectra due to the formation of multiple narrow subradiant resonances, and the multiple Fano resonances can be switched on and off by adjusting the polarization direction. Particularly, by modifying the geometry parameters, there is a large tunability of the modulation depth of each Fano resonance. Heptamer clusters comprising split nanorings are highly suitable for plasmon line shaping, and it is expected that they are useful for multiwavelength biosensing and surface-enhanced Raman scattering.