  We study the solutions to the scattering equations in various
quasi-multi-Regge regimes where the produced particles are ordered in rapidity.
We observe that in all cases the solutions to the scattering equations admit
the same hierarchy as the rapidity ordering, and we conjecture that this
behaviour holds independently of the number of external particles. In
multi-Regge limit, where the produced particles are strongly ordered in
rapidity, we determine exactly all solutions to the scattering equations that
contribute to the Cachazo-He-Yuan (CHY) formula for gluon scattering in this
limit. When the CHY formula is localised on these solutions, it reproduces the
expected factorisation of tree-level amplitudes in terms of impact factors and
Lipatov vertices. We also investigate amplitudes in various quasi-MRK. While in
these cases we cannot determine the solutions to the scattering equations
exactly, we show that again our conjecture combined with the CHY formula
implies the factorisation of the amplitude into universal buildings blocks for
which we obtain a CHY-type representation.
