We theoretically study the superconductivity in multiorbital superconductors based on a three-orbital tight-banding model. With appropriate values of the nearest-neighbour exchange $J_{1}^{alpha beta}$ and the next-nearest-neighbour exchange $J_{2}^{alpha beta}$, we find a two-dome structure in the $T_{c}-n$ phase diagram: one dome in the doping range $n<3.9$ where the superconducting (SC) state is mainly $s_{x^{2} y^{2}}$ component contributed by inter-orbital pairing, the other dome in the doping range $3.9<n<4.46$ where the SC state is mainly $s_{x^{2} y^{2}}+s_{x^{2}+y^{2}}$ components contributed by intra-orbital pairing. We find that the competition between different orbital pairing leads to two-dome SC phase diagrams in multiorbital superconductors, and different matrix elements of $J_{1}$ and $J_{2}$ considerably affect the boundary of two SC domes.
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