  We study the on-shell scattering amplitudes in quantum gravity for
high-energy collisions in the eikonal approximation. We first evaluate the
$n$-loop 2-particle scattering amplitude in the high energy and low momentum
transfer limit. We do so in a symmetrized manner by finding the contributions
of each of the particle worldines to the scattering amplitude and gluing them
together via the $n$ intermediate particle exchanges. In this limit on applying
the eikonal approximation and summing over all $n$-loop Feynman diagrams we
obtain a closed form for the 2 particle scattering amplitude. Finally, we
extend this approach to obtain a generalized eikonal approximation for
$N$-particle scattering at high energies and small momentum transfers. The
generalised form of the scattering amplitude can then be used to evaluate the
bound states of the system.
