In this work, we study the near-field heat transfer between composite nanostructures. It is demonstrated that thermally excited surface plasmon polaritons, surface phonon polaritons, and hyperbolic phonon polaritons in such composite nanostructures significantly enhance the near-field heat transfer. To further analyze the underlying mechanisms, we calculate energy transmission coefficients and obtain the near-field dispersion relations. The dispersion relations of composite nanostructures are substantially different from those of isolated graphene, silicon carbide (SiC) films, and SiC nanowire arrays due to the strong coupling effects among surface polaritonic modes. We identify four pairs of strongly coupled polaritonic modes with considerable Rabi frequencies in graphene/SiC film composite structures that greatly broaden the spectral peak. We confirm that near-field strong coupling effects between surface plasmon polaritons and hyperbolic phonon polaritons in the in-plane Reststrahlen band are different from those in the out-of-plane Reststrahlen band due to the different types of hyperbolicity. In addition, we analyze the effective tunability of the near-field heat transfer of graphene/SiC nanowire arrays composite structures by adjusting the chemical potential of graphene, the height and volume filling factor of the SiC nanowire arrays. This work provides a method to manipulate the near-field heat transfer with the use of strongly coupled surface polaritonic modes.