  We propose a systematic approximation scheme to calculate general $n$-point
$HSSA$ of open bosonic string theory. This stringy scaling loop expansion
contains finite number of vacuum diagram terms at each loop order of scattering
energy due to a vacuum diagram contraint and a topological graph constraint. In
addition, we calculate coefficient and give the vacuum diagram representation
and its Feynman rules for each term in the expansion of the $HSSA$. As an
application to extending our previous calculation of $n$-point leading order
stringy scaling behavior of $HSSA$, we explicitly calculate some examples of
$4$-point next to leading order stringy scaling violation terms.
