<p>The material point method (MPM) is an effective Lagrangian–Eulerian approach for analyzing solid mechanics problems involving large deformations, where particles in Lagrangian form move within a background grid in Eulerian form. However, the accuracy of MPM can be influenced by the grid cell size, where coarse grids often result in less precise outcomes. A common solution to this issue is local mesh refinement using transition elements and hanging nodes. In the MPM framework, the mesh grading material point method (MGMPM) has been proposed, utilizing traditional transition elements for local mesh refinement but has certain limitations. Its formulations depend on the placement of transition elements within the grid and impose restrictions on the number of hanging nodes along element boundaries, complicating general implementations. Additionally, some formulations introduce negative basis functions, which can cause numerical instabilities. To overcome these drawbacks, this paper introduces a new transition element based on alternative basis functions. With a single formulation, the proposed approach accommodates various placements of the transition element in the grid and any number of hanging nodes while mitigating the occurrence of negative basis functions. The transition element is implemented in the convected particle domain interpolation (CPDI) framework. An analytical proof demonstrates the preservation of continuity conditions and partition of unity in the proposed method. The efficacy of the method is demonstrated through three numerical examples for small- and large-deformation problems. A modified version of the G-vortex example is developed using the method of manufactured solution (MMS) for verification in large-deformation cases.</p>