Graphene exhibits great potential in near‑field thermal radiation regulation due to its tunable electronic properties and ability to support polariton excitation. In this work, symmetric and asymmetric near‑field thermal diode models composed of multilayer graphene‑covered silicon carbide (SiC) substrates are constructed, and the synergistic regulation of graphene layer number, chemical potential, and gap distance on the radiative heat flux and rectification ratio is systematically investigated. The results show that the modulation effect of graphene chemical potential and layer number on the heat flux strongly depends on the gap distance. Compared with the structure without graphene coating (SiC‑SiC) and the asymmetric graphene‑covered structure (GSiC‑SiC), the symmetric monolayer and multilayer graphene‑covered structures (MGSiC‑MGSiC) significantly enhance the radiative heat flux at small gap distances (d < 300 nm), and heat flux presents a peak as the chemical potential rises. In the gap distance range of 50‑500 nm, the radiative heat flux increases with the graphene layer number, but the enhancement gradually slows down as the layer number further increases. For asymmetric graphene‑covered structures (GSiC‑SiC, MGSiC‑SiC, MGSiC‑GSiC), increasing the chemical potential or the layer number is detrimental to the enhancement of the radiative heat flux at small gap distance (d < 300 nm); at large gap distance (d > 300 nm), the modulation effect of graphene chemical potential and layer number on the heat flux tends to zero. For the asymmetric graphene‑covered structure (MGSiC‑SiC), reducing the chemical potential (0.5 eV, 0.3 eV, 0.1 eV) and decreasing the layer number (from 4 to 1) effectively improve the thermal rectification ratio. Numerical calculations show that when the graphene layer number, chemical potential and gap distance are 1, 0.1 eV, and 30 nm, respectively, the rectification ratio of the MGSiC‑SiC structure reaches 0.155. For the MGSiC‑GSiC structure, as the layer number increases from 1 to 4, the maximum rectification ratio of 0.035 is achieved at 3 layers, 100 nm and a chemical potential of 0.1 eV. For all asymmetric structures (GSiC‑SiC, MGSiC‑SiC, MGSiC‑GSiC), the maximum rectification ratios appear in the near‑field region. These results indicate that a smaller gap distance, lower chemical potential, and fewer graphene layers are favorable for achieving superior thermal rectification performance in asymmetric graphene‑covered structures. This study reveals the synergistic regulation mechanism among graphene layer number, chemical potential, and near‑field effects, providing theoretical guidance for the design of high‑performance near‑field thermal rectifiers.