  There are many open questions surrounding the characterisation of groups with
context-sensitive word problem. Only in 2018 was it shown that all finitely
generated virtually Abelian groups have multiple context-free word problems,
and it is a long-standing open question as to where to place the word problems
of hyperbolic groups in the formal language hierarchy. In this paper, we
introduce a new language class called the parallel hyperedge replacement string
languages, show that it contains all multiple context-free and ET0L languages,
and lay down the foundations for future work that may be able to place the word
problems of many hyperbolic groups in this class.
