  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.
