In scientific visualization, despite the significant advances of deep learning for data generation, researchers have not thoroughly investigated the issue of data translation. We present a new deep learning approach called generalized multivariate translation (GMT) for multivariate time-varying data analysis and visualization. Like V2V, GMT assumes a preprocessing step that selects suitable variables for translation. However, unlike V2V, which only handles one-to-one variable translation during training and inference, GMT enables one-to-many and many-to-many variable translation in the same framework. We leverage the recent StarGAN design from multi-domain image-to-image translation to achieve this generalization capability. We experiment with different loss functions and injection strategies to explore the best choices and leverage pre-training for performance improvement. We compare GMT with other state-of-the-art methods (i.e., Pix2Pix, V2V, StarGAN). The results demonstrate the overall advantage of GMT in translation quality and generalization ability.