Genetically modified or ‘transgenic’ mice are a routine experimental tool in biomedical research, commonly produced by injecting DNA into one-cell embryos. These animals were independently invented in 1980 by multiple university groups in the United States and Europe that combined expertise in mouse developmental biology and recombinant DNA techniques, or ‘genetic engineering’. In this article, I examine this multiple invention and argue that research strategies, experimental practices, and funding arrangements that led to transgenic mice are best described as tinkering. These creative and speculative endeavors, combined with partial knowledge of what was happening in competing laboratories, created a fruitful atmosphere for research which led to the multiple invention. The tinkering was, however, underpinned by infrastructures that were crucial to success, some long established, such as mouse supply or embryological tools, and some emerging, such as the informal exchange of isolated genes.