Most Probable Explanation (MPE) is a fundamental problem in statistical relational artificial intelligence. In the context of Probabilistic Answer Set Programming (PASP), solving MPE is still an open research problem. In this paper, we present three novel approaches for solving the MPE task in PASP that are based on: i) Algebraic Model Counting, ii) Answer Set Programming (ASP), and iii) ASP with quantifiers (ASP(Q)). These approaches are implemented and evaluated against existing solvers across different datasets and configurations. Empirical results demonstrate that the novel solutions consistently outperform existing alternatives for non-stratified programs.