Efficient object manipulation strategies have significant impact in automation applications. In this work, the stack rearrangement in tabletop settings is studied, with a focus on augmenting the task planning domain with richer nonprehensile aggregating actions, in particular the toppling of objects from a stack to the table. Toppling can compress long sequences of intermediate relocations. Computed plans need to interleave pick-and-place actions with topple throughout its plan based on the problem. In order to generate the task plan and model an abstraction to compute solutions that include both pick-and-place and topple actions, a novel aggregating gadget for topple is introduced. Using this directed graphical abstraction, candidate task plan computation becomes a variant of the pebble motion problem, treating objects as pebbles. Benchmarks are then reported in a IsaacSim-based physics simulation. Results highlight clear benefits of achieving faster execution than solely using pick-and-place actions. Though this work primarily investigates the topple action, we demonstrate that similar abstractions can model other aggregating actions of interest, like scoop. The current work provides a preliminary, strong indication of the promising benefits of abstractions for rich object interactions in manipulation applications.