On soficity for certain fundamental groups of graphs of groups

In this note we study a family of graphs of groups over arbitrary base graphs where (1) all vertex groups are isomorphic to a fixed countable sofic group [Formula: see text], (2) all edge groups [Formula: see text] are such that the embeddings of [Formula: see text] into [Formula: see text] are identical everywhere. We prove soficity for this family of groups under a flexible technical hypothesis for [Formula: see text] called [Formula: see text]-sofically-separable. This proves soficity for group doubles [Formula: see text], where [Formula: see text] is an arbitrary separable subgroup and [Formula: see text] is countable and sofic. This includes arbitrary finite index group doubles of sofic groups among various other examples.