May happen in Parallel (MHP) analysis is one of the most foundational analysis in the context of programs written in parallel languages like Java. The current known techniques for doing MHP analysis of Java applications suffer from two main challenges: (i) scalability to real world large applications, (ii) precision in the presence of complex programs. In this manuscript, we address these two issues with a goal to make MHP analysis for Java applications a practical option. We propose a new MHP analysis scheme called GRIP-MHP. It includes techniques to reduce time taken for performing MHP analysis significantly; it does so by using novel schemes to reduce the size of the input graph (representing the original application). GRIP-MHP also addresses many drawbacks in existing techniques, thereby improving the applicability and precision of MHP analysis for real-world Java applications. We implemented GRIP-MHP in the Soot compiler framework. our experiments show that GRIP-MHP runs successfully in reasonable time on all the tested benchmarks in DaCapo and Renaissance benchmarks (geomean 31.96$\times$ improvement, over prior work). We find that GRIP-MHP also leads to improvements in precision of the analysis results (geomean, 1.88$\times$ improvement, over prior work).