Collective optoelectronic phenomena such as plasmons and phonon polaritons can drive processes in many branches of nanoscale science. Classical physics predicts that a perfect thermal emitter operates at the black body limit. Numerous experiments have shown that surface phonon polaritons allow emission two orders of magnitude above the limit at a gap distance of ≈50 nm. This work shows that a supported multilayer graphene structure improves the state of the art by around one order of magnitude with a ≈1129-fold-enhancement at a gap distance of ≈55 nm. Coupled surface plasmon polaritons at mid- and far-infrared frequencies allow for near-unity photon tunneling across a broad swath of k-space enabling the improved result. Electric tuning of the Fermi-level allows for the detailed characterization and optimization of the colossal nanoscale heat transfer.