Assumption-based argumentation (ABA) is one of the main general frameworks for structured argumentation. Dispute derivations for ABA allow for evaluating claims in a dialectical manner: i.e. on the basis of an exchange of arguments and counter-arguments for a claim between a proponent and an opponent of the claim. Current versions of dispute derivations are geared towards determining (credulous) acceptance of claims w.r.t. the admissibility-based semantics that ABA inherits from abstract argumentation. Relatedly, they make use of backwards or top down reasoning for constructing arguments. In this work we define flexible dispute derivations with forward as well as backward reasoning allowing us, in particular, to also have dispute derivations for finding admissible, complete, and stable assumption sets rather than only determine acceptability of claims. We give an argumentation-based definition of such dispute derivations and a more implementation friendly alternative representation in which disputes involve exchange of claims and rules rather than arguments. These can be seen as elaborations on, in particular, existing graph-based dispute derivations on two fronts: first, in also allowing for forward reasoning; second, in that all arguments put forward in the dispute are represented by a graph and not only the proponents.