We proposed herein a multi-solver domain decomposition method (MS-DDM), and applied it to compute the mutual couplings among multiple antennas mounted on a large air platform at Ku-band, 15 GHz to be exact. The fundamental strategy of the proposed MS-DDM is to decompose the entire computational domain into many sub-regions based on the local material properties and geometrical features. Subsequently, we employ the most suitable computational electromagnetic (CEM) technique for each of the sub-regions. Moreover, the coupling between well-separated sub-regions is implemented through Stratton-Chu representation formulas. However, for the touching interfaces between neighboring sub-regions, a Robin transmission condition is introduced to mitigate the troublesome self-integral terms with weak singular kernels. The proposed MS-DDM is therefore well suited for modeling multiple antennas conformally mounted on a large platform, where touching sub-regions are usually unavoidable. Furthermore, by using the proposed MS-DDM framework, multiple existing CEM solvers, such as integral equation domain decomposition method(IE-DDM), the finite element domain decomposition method (FE-DDM), and generalized combined field integral equation (GCFIE) method have been successfully integrated with few minor modifications.