Most MEMS piezoelectric vibration energy harvesters involve either cantilever-based topologies, doubly-clamped beams or membrane structures. While these traditional designs offer simplicity, their frequency response for broadband excitation are typically inadequate. This paper presents a new integrated cantilever-on-membrane design that attempts to both optimise the strain distribution on a piezoelectric membrane resonator and improve the power responsiveness of the harvester for broadband excitation. While a classic membrane-based resonator has the potential to theoretically offer wider operational frequency bandwidth than its cantilever counterpart, the addition of a centred proof mass neutralises its otherwise high strain energy regions. The proposed topology addresses this issue by relocating the proof mass onto subsidiary cantilevers and integrates the merits of both the membrane and the cantilever designs. When experimentally subjected to a band-limited white noise excitation, up to approximately two folds of power enhancement was observed for the new membrane harvester compared to a classic plain membrane device.