  We develop an operator formalism to compute scattering amplitudes of
arbitrary bosonic string states in the background of many D-branes.
Specifically, we construct a suitable boundary state which we use to saturate
the multi-Reggeon vertex in order to obtain the generator of multi-membrane
scattering amplitudes. We explicitly show that the amplitudes with $h$ parallel
D-branes are similar to amplitudes with $h-1$ open string loops.
