The Universal Variability Language (UVL) was designed with high extensibility in mind. Still, the development of new extensions necessitates a precise semantic definition and a transformation into a solver-specific encoding for their analysis. Such a transformation is challenging due to the difference in levels of abstraction, making the resulting encoding hard to understand. Moreover, the transformation itself becomes difficult to be extended. In this paper, we propose a simplified process for UVL extension by (1) analyzing the semantics of UVL and (2) providing a transformation of UVL models into an Answer Set Programming (ASP) encoding. We show the effectiveness of our approach in the exemplary extension of UVL with new concepts: attribute domains, derived attributes and scoped aggregates. Finally, we compare our approach to the conventional flattening of extensions to the existing UVL language levels, showing less implementation effort and better readability.