We develop an operator formalism to compute scattering amplitudes of a
rbitrary bosonic string states in the background of many D-branes. Spe
cifically, we construct a suitable boundary state which we use to satu
rate the multi-Reggeon vertex in order to obtain the generator of mult
i-membrane scattering amplitudes. We explicitly show that the amplitud
es with h parallel D-branes arc similar to amplitudes with h-1 open st
ring loops. (C) 1997 Elsevier Science B.V.