We derive two identities for multiple basic hyper-geometric series associated with the unitary $U(n+1)$ group. In order to get the two identities, we first present two known $q$-exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two $U(n+1)$$q$-Chu-Vandermonde summations established by Milne, we arrive at our...