  We discuss giant graviton expansions for the Schur index of ${\cal N}=4$
$U(N)$ SYM with the insertion of Wilson lines of the fundamental and the
anti-fundamental representations. We first propose a double-sum giant graviton
expansion and numerically confirm that it correctly reproduces the
line-operator index. We also find that it reduces to a simple-sum expansion
when we treat the index as a Taylor series with respect to a specific fugacity.
