Answer set programming (ASP) solvers have advanced in recent years, with a variety of different specialisation and overall development. Thus, even more complex and detailed programs can be solved. A side effect of this development are growing solution spaces and the problem of how to find those answer sets one is interested in. One general approach is to give an overview in form of a small number of highly diverse answer sets. By choosing a favourite and repeating the process, the user is able to leap through the solution space. But finding highly diverse answer sets is computationally expensive. In this paper we introduce a new approach called Tunas for Trade Up Navigation for Answer Sets to find diverse answer sets by reworking existing solution collections. The core idea is to collect diverse answer sets one after another by iteratively solving and updating the program. Once no more answer sets can be added to the collection, the program is allowed to trade answer sets from the collection for different answer sets, as long as the collection grows and stays diverse. Elaboration of the approach is possible in three variations, which we implemented and compared to established methods in an empirical evaluation. The evaluation shows that the Tunas approach is competitive with existing methods, and that efficiency of the approach is highly connected to the underlying logic program.