The overwhelming majority of microelectromechanical piezoelectric vibration energy harvesting topologies have been based on cantilevers, doubly-clamped beams or basic membranes. While these conventional designs offer simplicity, their broadband response are thus far limited. This paper investigates the feasibility of a new integrated cantilever-on-membrane design that explores the optimisation of piezoelectric strain distribution and improvement of the broadband power output. While a classic membrane has the potential to offer a broader resonant peak than its cantilever counterpart, the inclusion of a centred proof mass compromises its otherwise high strain energy regions. The proposed topology addresses this issue by relocating the proof mass onto subsidiary cantilevers and combines the merits of both the membrane and the cantilever designs. Numerical simulations, constructed using fitted values based on finite element models, were used to investigate the broadband response of the proposed design in contrast to a classic plain membrane. Experimentally, when subjected to a band-limited white noise excitation, the new cantilevers-on-membrane harvester exhibited nearly two fold power output enhancement when compared to a classic plain membrane harvester of a comparable size.