The GEANT4 toolkit is used extensively in high energy physics to simulate the passage of particles through matter and to predict effects such as detector efficiencies and smearing. GEANT4 uses many underlying models to predict particle interaction kinematics, and uncertainty in these models leads to uncertainty in high energy physics measurements. The GEANT4 collaboration recently made free parameters in some models accessible through partnership with GEANT4 developers. We present a study of the impact of varying parameters in three GEANT4 hadronic physics models on agreement with thin target datasets and describe fits to these datasets using the Professor model tuning framework [1]. We find that varying parameters produces substantially better agreement with some datasets, but that more degrees of freedom are required for full agreement. This work is a first step towards a common framework for propagating uncertainties in GEANT4 models to high energy physics measurements, and we outline future work required to complete that goal.