While Answer-Set Programming (ASP) is a prominent approach to declarative problem solving, optimisation problems can still be a challenge for it. Large-Neighbourhood Search (LNS) is a metaheuristic for optimisation where parts of a solution are alternately destroyed and reconstructed that has high but untapped potential for ASP solving. We present a framework for LNS optimisation in answer-set solving in which neighbourhoods can be specified either declaratively as part of the ASP encoding or automatically generated by code. To effectively explore different neighbourhoods, we focus on multi-shot solving as it allows to avoid program regrounding. We illustrate the framework on different optimisation problems some of which are notoriously difficult, including shift planning and a parallel machine scheduling problem from semi-conductor production, which demonstrate the effectiveness of the LNS approach.