  High-energy massless gravitational scattering in ${\cal N}=8$ supergravity
was recently analyzed at leading level in the deflection angle, uncovering an
interesting connection between exponentiation of infrared divergences in
momentum space and the eikonal exponentiation in impact parameter space. Here
we extend that analysis to the first non trivial sub-leading level in the
deflection angle which, for massless external particles, implies going to two
loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the
leading eikonal, we see that the factorisation of the momentum space amplitude
into the exponential of the one-loop result times a finite remainder hides some
basic simplicity of the impact parameter formulation. For the conservative part
of the process, the explicit outcome is infrared (IR) finite, shows no
logarithmic enhancement, and agrees with an old claim in pure Einstein gravity,
while the dissipative part is IR divergent and should be regularized, as usual,
by including soft gravitational bremsstrahlung. Finally, using recent
three-loop results, we test the expectation that eikonal formulation accounts
for the exponentiation of the lower-loop results in the momentum space
amplitude. This passes a number of highly non-trivial tests, but appears to
fail for the dissipative part of the process at all loop orders and
sufficiently subleading order in $\epsilon$, hinting at some lack of
commutativity of the relevant infrared limits for each exponentiation.
