  We calculate, using the group theoretic approach to string theory, the tree
and one loop scattering of four open and closed arbitrary bosonic string
states. In the limit of high energy, but fixed angle, the multi-string vertex
at tree and one loop levels that we find takes a very simple form. We propose,
and present arguments for, a form for the high energy multi-string vertex at
all loops; in particular we give a path integral derivation of this vertex. Our
results agree with those of Gross and Mende for tachyon scattering amplitudes,
but those for any other string scattering are substantially different from that
discussed in reference [5]. We also develop some of the technology used in the
group theoretic method to compute loop corrections.
