  Recently, we formulated the $q$-Garnier system and its variations as
translations of an extended affine Weyl group of type $A^{(1)}_{2n+1}\times
A^{(1)}_1\times A^{(1)}_1$. On the other hand, those systems admit particular
solutions in terms of the basic hypergeometric series ${}_{n+1}\phi_n$. In this
article, we investigate an action of the extended affine Weyl group on
${}_{n+1}\phi_n$.
