Like conventional software projects, projects in model-driven software engineering require adequate management of multiple versions of development artifacts, importantly allowing living with temporary inconsistencies. In previous work, multi-version models for model-driven software engineering have been introduced, which allow checking well-formedness and finding merge conflicts for multiple versions of a model at once. However, also for multi-version models, situations where different artifacts, that is, different models, are linked via automatic model transformations have to be handled. In this paper, we propose a technique for jointly handling the transformation of multiple versions of a source model into corresponding versions of a target model, which enables the use of a more compact representation that may afford improved execution time of both the transformation and further analysis operations. Our approach is based on the well-known formalism of triple graph grammars and the aforementioned encoding of model version histories called multi-version models. In addition to batch transformation of an entire model version history, the technique also covers incremental synchronization of changes in the framework of multi-version models. We show the correctness of our approach with respect to the standard semantics of triple graph grammars and conduct an empirical evaluation to investigate the performance of our technique regarding execution time and memory consumption. Our results indicate that the proposed technique affords lower memory consumption and may improve execution time for batch transformation of large version histories, but can also come with computational overhead in unfavorable cases.