  In this paper we find a host of boost operators for a very general choice of
coproducts in AdS_3-inspired scattering theories, focusing on the massless
sector, with and without an added trigonometric deformation. We find that the
boost coproducts are exact symmetries of the R-matrices we construct, besides
fulfilling the relations of modified Poincare' - type superalgebras. In the
process, we discover an ambiguity in determining the boost coproduct which
allows us to derive differential constraints on our R-matrices. In one
particular case of the trigonometric deformation, we find a non-coassociative
structure which satisfies the axioms of a quasi-Hopf algebra.
