Modulating near-field radiative heat transfer (NFRHT) with a high dynamic range is challenging in nanoscale thermal science and engineering. Modulation depths [(maximum value - minimum value)/(maximum value + minimum value) × 100%] of ≈2% to ≈15.7% have been reported with matched modes, but breaking the constraint of mode matching theoretically allows for higher modulation depth. We demonstrate a modulation depth of ≈32.2% by a pair of graphene-covered SU8 heterostructures at a gap distance of ≈80 nm. Dissimilar Fermi levels tuned by bias voltages enable mismatched surface plasmon polaritons which improves the modulation. The modulation depth when switching from a matched mode to a mismatched mode is ≈4.4-fold compared to that when switching between matched modes. This work shows the importance of symmetry in polariton-mediated NFRHT and represents the largest modulation depth to date in a two-body system with fixed gap distance and temperature.