Stabilisers, such as surfactants, polymers and polyaromatic molecules, offer an effective way to produce graphene dispersions in water by Liquid Phase Exfoliation (LPE), without degrading the properties of graphene. In particular, pyrene derivatives provide better exfoliation efficiency than traditional surfactants and polymers. A stabiliser is expected to be relatively soluble in order to disperse hydrophobic graphene in water. Here, we show that exfoliation can also be achieved with insoluble pyrene stabilisers if appropriately designed. In particular, bis-pyrene stabilisers (BPSs) functionalised with pyrrolidine provide higher exfoliation efficiency and percentage of single layers, as compared to traditional pyrene derivatives, under the same experimental conditions. This is attributed to the enhanced interactions between BPS and graphene, provided by the presence of two pyrene binding groups. This approach is therefore attractive not only to produce highly concentrated graphene, but also to use graphene to disperse insoluble molecules in water. The enhanced adsorption of BPS on graphene, however, is reflected in higher toxicity towards human epithelial bronchial immortalized cells, limiting the use of this material for biomedical applications.