Several studies have suggested that the motor system takes advantage of a coordinate system when learning a novel sensorimotor environment. Such investigations, however, have not distinguished between initial preferences of a coordinate system versus possible changes due to learning. Here, we present experimental methods that specifically entertain the possibility of multiple coordinate systems during generalization. Subjects trained with their right arm on a viscous force field. We evaluated their performances for both arms in an untrained workspace before and after training using three fields, each representing extrapolation with a candidate coordinate system. Surprisingly, our results showed evidence of improvement (pre to post) in all fields for both limbs. These findings are consistent with the hypothesis of multiple, simultaneous coordinate systems involved in generalization. We also investigated how feedback might affect the results and found in several cases that performance was better for visual displays that were aligned with the limb (in first person) versus non-aligned.