Graphene is a nanomaterial that is well-suited for building neurosensors due to its biocompatibility, flexibility, and good electrical properties. Furthermore, prior research has shown graphene field-effect transistors can measure action potentials of in-vivo and in-vitro neurons. We investigate unique uses for graphene field-effect transistors (FETs) in neurosensing applications. We first show that our graphene FETs are capable of measuring action potentials from in-vitro cells plated on the devices. Then we explore a free-floating graphene FET released from the substrate that can be lowered onto individual cells for targeted single-neuron measurements. Next, we developed an array of graphene FETs with multiplexing (wire sharing) for taking simultaneous measurements of many neurons. Based on the performance of our prototype devices, we show that this is a scalable technology that be used to operate arrays of more than 1000 sensors with fewer than 100 input/output wires. Lastly, we interfaced our graphene FET array with a custom integrated circuit chip that amplifies and digitizes the multiplexed signals.