  We formulate a strategy for computing the complete set of non-perturbative
corrections to closed string scattering in $c=1$ string theory from the
worldsheet perspective. This requires taking into account the effect of
multiple ZZ-instantons, including higher instantons constructed from ZZ
boundary conditions of type $(m,1)$, with a careful treatment of the measure
and contour in the integration over the instanton moduli space. The only a
priori ambiguity in our prescription is a normalization constant ${\cal N}_{m}$
that appears in the integration measure for the $(m,1)$-type ZZ instanton, at
each positive integer $m$. We investigate leading corrections to the closed
string reflection amplitude at the $n$-instanton level, i.e. of order
$e^{-n/g_s}$, and find striking agreement with our recent proposal on the
non-perturbative completion of the dual matrix quantum mechanics, which in turn
fixes ${\cal N}_{m}$ for all $m$.
