OpenMP is the de-facto standard for parallel programming on shared-memory systems. The choice of scheduling methods in OpenMP work sharing parallel loops is a critical aspect for performance, especially for computationally-intensive and irregular parallel loops. In this work, we explore loop scheduling enhancements in OpenMP. Three loop scheduling choices are covered today in the OpenMP standard: static, guided, and dynamic. These are no longer sufficient to address the load imbalance that adversely affects the execution of computationally-intensive and irregular parallel loops. In this work, we present a generic methodology for exploring loop scheduling enhancements in OpenMP that allows the implementation, testing, and usage of additional (more advanced) loop scheduling choices in OpenMP runtime systems. We showcase the methodology by enhancing the LLVM OpenMP runtime with an additional dynamic loop self-scheduling (DLS) technique, known to offer superior load balancing over the existing OpenMP scheduling choices for computationally-intensive and irregular parallel loops. We analyze the overhead of the (existing and newly added) OpenMP loop scheduling methods and show that the proposed methodology incurs no additional overhead. We also study the performance of four benchmarks using the enhanced LLVM OpenMP runtime. The results show that, for the four benchmarks considered, no single loop scheduling strategy outperforms the others. The newly implemented DLS technique provides an additional opportunity for improved execution time with the LLVM OpenMP runtime, which was not possible before this study. Our newly implemented scheduling strategy is competitive with the best previous scheduling choices. This methodology for exploring loop scheduling enhancements in OpenMP lays the foundation for further loop scheduling additions and explorations in OpenMP.