When a new sensorimotor mapping is learned through practice, learning commonly transfers to unpracticed regions of task space, that is, generalization ensues. Does generalization reflect fixed properties of movement representations in the nervous system and thereby limit what visuomotor mappings can and cannot be learned? Or does what needs to be learned determine the shape of generalization? We used the broad generalization properties of visuomotor gain adaptation to address these questions. Adaptation to a single gain for reaching movements is known to generalize broadly across movement directions. By training subjects on two different gains in two directions, we set up a potential conflict between generalization patterns: if generalization of gain adaptation indicates fixed properties of movement amplitude encoding, then learning two different gains in different directions should not be possible. Conversely, if generalization is flexible, then it should be possible to learn two gains. We found that subjects were able to learn two gains simultaneously, although more slowly than when they adapted to a single gain. Analysis of the resulting double-gain generalization patterns, however, unexpectedly revealed that generalization around each training direction did not arise de novo, but could be explained by a weighted combination of single-gain generalization patterns, in which the weighting takes into account the relative angular separation between training directions. Our findings therefore demonstrate that the mappings to each training target can be fully learned through reweighting of single-gain generalization patterns and not through a categorical alteration of these functions. These results are consistent with a modular decomposition approach to visuomotor adaptation, in which a complex mapping results from a combination of simpler mappings in a "mixture-of-experts" architecture.