Mixed networks of conducting and non-conducting nanoparticles show promise in a range of applications where fast charge transport is important. While the dependence of network conductivity on the conductive mass fraction (Mf) is well understood, little is known about the Mf-dependence of mobility and carrier density. This is particularly important as the addition of graphene might lead to increases in the mobility of semiconducting nanosheetnetwork transistors. Here, we use electrolytic gating to investigate the transport properties of spray-coated composite networks of graphene and WS2 nanosheets. As the graphene Mf is increased, we find both conductivity and carrier density to increase in line with percolation theory with percolation thresholds (~8 vol%) and exponents (~2.5) consistent with previous reporting. Perhaps surprisingly, we find the mobility increases modestly from ~0.1 cm 2 /Vs (for a WS2 network) to ~0.3 cm 2 /Vs (for a graphene network) which we attribute to the similarity between WS2-WS2 and graphene-graphene junction resistances. In addition, we find both the transistor on-and off-currents to scale with Mf according to percolation theory, changing sharply at the percolation threshold. Through fitting, we show that only the current in the WS2 network changes significantly upon gating. As a result, the on-off ratio falls sharply at the percolation threshold from ~10 4 to ~2 at higher Mf. Reflecting on these results, we conclude that the addition of graphene to a semiconducting network is not a viable strategy to improve transistor performance as it reduces the on:off ratio far more than it improves the mobility.