Extended discontinuous Galerkin (XDG) methods stand as advanced high-order techniques designed for addressing multiphase problems characterized by jumps and kinks at interfaces. When dealing with interfaces, XDG methods adopt a sharp interface approach and implement a cut cell structure, in which different phases are embedded into a Cartesian grid to facilitate the mesh generation process. However, in such methods, arbitrary small cells occur due to the intersections of background cells with interfaces and lead to discretization difficulties due to their diminutive sizes. Furthermore, topological inconsistencies may arise in different time steps when the embedded phases change in size over time. To account for these issues associated with small-cut cells and topological changes, a cell agglomeration approach is employed in the XDG method and tailored for large-scale simulations. This approach merges problematic cells with suitable neighbors and has been deemed as a simple and convenient method. However, it is important to note that cell agglomeration becomes challenging in three-dimensional space where there is a high degree of neighborship between cells. Furthermore, it can create cumbersome problems in large computational simulations such as forming agglomeration chains and ineffective parallel information exchange. In our work, we provide a comprehensive strategy for the typical issues addressed to cell agglomeration in three-dimensional and multiprocessor simulations. The proposed strategy is implemented into the open-source software package BoSSS and tested with large-scale simulations of immersed boundary and two-phase flows.