In this paper, we show a proof-of-concept method to parallelise phonon microscopy measurements for cell elasticity imaging by demonstrating a 3-fold increase in acquisition speed which is limited by current acquisition hardware. Phonon microscopy is based on time-resolved Brillouin scattering, which uses a pump–probe method with asynchronous optical sampling (ASOPS) to generate and detect coherent phonons. This enables access to the cell elasticity via the Brillouin frequency with sub-optical axial resolution. Although systems based on ASOPS are typically faster compared to the ones built with a mechanical delay line, they are still very slow to study real time changes at the cellular level. Additionally, the biocompatibility is reduced due to long light exposure and scanning time. Using a multi-core fibre bundle rather than a single channel for detection, we acquire 6 channels simultaneously allowing us to speed-up measurements, and open a way to scale-up this method.