This paper presents the design exploration of a basic cascode circuit (CAS) targeted to increase the intrinsic gain A# of a graphene field-effect-transistor (GFET) by decreasing its output conductance go. First, the parameters of a large-signal compact-model, based on drift-diffusion carrier transport, are fit to measurements carried on 2 CVD GFETs, fabricated independently by different research groups. Second, CAS circuits are simulated to perform a design exploration and provide design guidelines. Third, CAS circuits are fabricated and consequently measured. Performance metrics are provided in terms of go, transconductance gm and hence A#. Against these metrics, a quantitative comparison between CAS and GFET is performed and conclusions are derived.