Overdecomposition has emerged as a powerful and sometimes essential technique in parallel programming. Many application domains or frameworks, including those based on adaptive mesh refinements, or tree codes use it. Charm++ is a parallel programming system which has demonstrated the utility of overdecomposition for many applications and in multiple contexts. However, the emergence of GPGPUs as a dominant compute component has created some real and perceived challenges for this paradigm, especially regarding the higher overhead brought about by overpartitioning -- having multiple objects assigned to the same GPGPU device. We address this issue as well as the issue of portability by developing techniques and software that demonstrate that overdecomposition can be efficiently and productively supported on combinations of GPU vendor types, and interconnection networks.