  A recently developed n-particle scattering theory for wedge-local quantum
field theories is applied to a class of models described and constructed by
Grosse, Lechner, Buchholz, and Summers. In the BLS-deformation setting we
establish explicit expressions for n-particle wave operators and the S-matrix
of ordered asymptotic states, and we show that ordered asymptotic completeness
is stable under the general BLS-deformation construction. In particular the
(ordered) Grosse-Lechner S-matrices are non-trivial also beyond two-particle
scattering and factorize into 2-particle scattering processes, which is an
unusual feature in space-time dimension d > 1 + 1. Most notably, the
Grosse-Lechner models provide the first examples of relativistic (wedge-local)
QFT in space-time dimension d > 1 + 1 which are interacting and asymptotically
complete.
