We follow up our work  concerning the
formation of trapped surfaces. We provide a considerable extension of
our result there on pre-scared surfaces to allow for the formation of a surface with multiple pre-scared angular regions which, together, can cover an arbitrarily large portion of the surface. In a forthcoming paper we plan to show that once a significant part of the surface is pre-scared, it can be additionally
deformed to produce a bona-fide trapped surface.