  Groups associated to surfaces isogenous to a higher product of curves can be
characterised by a purely group-theoretic condition, which is the existence of
a so-called ramification structure. G\"{u}l and Uria-Albizuri showed that
quotients of the periodic Grigorchuk-Gupta-Sidki groups, GGS-groups for short,
admit ramification structures. We extend their result by showing that quotients
of generalisations of the GGS-groups, namely multi-EGS groups, also admit
ramification structures.
