Many recent studies of dynamics of formal argumentation in AI focus on the well-known formalism of argumentation frameworks (AFs). Despite their use-fulness in many areas of argumentation, their abstract notion of arguments creates a barrier for operators that modify a given AF, namely in the case that dependencies between arguments have been abstracted away that might be subsequently missed. In this paper we aim to support development of dynamic operators on formal models in abstract argumentation by providing constraints imposed on the modification of the structure that can be used to incorporate information that has been abstracted away. Towards a broad reach, we base our results on the general formalism of abstract dialectical frameworks (ADFs) in abstract argumentation, and study the complexity of the proposed structural constraints. To show applicability, we adapt an extension enforcement operator on AFs to ADFs that is allowed to only add support relations between arguments. We show feasibility of our approach by an experimental evaluation of an implementation of this operator.